JP7777336B2 - Estimation device, wireless communication system including the same, and program for causing a computer to execute the same - Google Patents

Description

Article 30, Paragraph 2 of the Patent Act applies. "Matrix Factorization-Based RSS Interpolation for Radio Environment Prediction" was published in IEEE WIRELESS COMMUNICATIONS LETTERS, VO. 10, NO. 7, July 2021. "Study on Propagation Path Matrix Prediction in IRS-Assisted MIMO-OFDM Systems" was published in IEICE Technical Report SR2021-85 (2022-3).

This invention relates to an estimation device, a wireless communication system including the same, and a program for causing a computer to execute the same.

Next-generation communications standards require the creation of a communications infrastructure that will enable access to all people, information, and things anywhere, both domestically and internationally, while enhancing the high speed, large capacity, low latency, and multiple connection capabilities that are characteristic of fifth-generation mobile communications systems (5G).

High-frequency radio waves cannot be expected to propagate beyond line of sight, resulting in weak spots. For this reason, there has been active research into technology that solves the problem of high-frequency radio waves by using an intelligent reflecting surface (IRS), which is made up of multiple passive reflecting elements whose reflection characteristics can be dynamically changed (Non-Patent Document 1). By appropriately changing the reflection characteristics of each element and creating a radio wave propagation path that bypasses obstacles, stable communication can be achieved even beyond line of sight.

Because IRS essentially acts as an electromagnetic wave reflector and does not contain high-frequency circuits, it also has the advantage of consuming significantly less power than conventional multi-hop communications used to expand coverage.

Q. Wu and R. Zhang, “Towards Smart and Reconfigurable Environment: Intelligent Reflecting Surface Aided Wireless Network,” IEEE Commun. Mag., vol. 58, no. 1, pp. 106-112, 2020. E. Basar, M. Di Renzo, J. De Rosny, M. Debbah, M. S. Alouini, and R. Zhang, “Wireless Communications Through Reconfigurable Intelligent Surfaces,” IEEEAccess, vol. 7, no. June 2018, pp. 116753-116773, 2019. Y. Yang, B. Zheng, S. Zhang, and R. Zhang, “Intelligent reflecting surface meets OFDM: Protocol design and rate maximization,” 2019.[Online]. Available: https://arxiv.org/abs/1906.09956. B. Zheng and R. Zhang, “Intelligent Reflecting Surface-Enhanced OFDM: Channel Estimation and Reflection Optimization,” IEEE Wirel. Commun. Lett., vol. 9, no. 4, pp. 518-522, 2020. Q.-U.-A. Nadeem, H. Alwazani, A. Kammoun, A. Chaaban, M.Debbah, and M.-S. Alouini, “Intelligent Reflecting Surface-Assisted Multi-User MISO Communication: Channel Estimation and Beamforming Design,” IEEE Open J. Commun. Soc., vol. 1, no. March, pp. 661-680, 2020. B. Zheng, C. You, and R. Zhang, “Fast Channel Estimation for IR-S Assisted OFDM,” IEEE Wirel. Commun. Lett., vol. 10, no. 3, pp.580-584, 2021. W. Jiang and H. Di. Schotten, “A Comparison of Wireless Channel Predictors: Artificial Intelligence Versus Kalman Filter,” IEEE Int. Conf. Commun., 2019. Y. Yang, B. Zheng, S. Zhang, and R. Zhang, “Intelligent Reflecting Surface Meets OFDM: Protocol Design and Rate Maximization,” IEEE Trans. Commun., vol. 68, no. 7, pp. 4522-4535, Jul. 2020.

However, in a wireless communication system using an IRS (an IRS-assigned system), in order to optimize the reflection coefficients for all reflecting elements on the IRS, it is necessary to estimate a huge number of propagation paths, each of which exists as a combination of a transmitting antenna, each reflecting element, and a receiving antenna (Non-Patent Documents 2 to 6).

Propagation path estimation typically involves using a known training signal between the transmitter and receiver. However, in an IRS-assist system, because numerous propagation paths exist, a long training period is required to estimate these propagation path groups. Furthermore, because the receiver must provide feedback on the propagation path group estimates or reflection pattern information calculated from the estimates to the IRS, a longer lag is likely to occur between the time channel estimation (propagation path estimation) is performed and data transmission compared to systems that do not use IRS. When a wireless terminal moves, the propagation path inevitably fluctuates, and if there is a large lag from the time estimation is performed, controlling the IRS based on past channel estimates (propagation path estimates) will not maximize its performance.

Accordingly, an embodiment of the present invention provides an estimation device that can suppress the discrepancy caused by the lag between the estimated time of the propagation path between the transmitter and receiver and the transmission time.

Furthermore, according to an embodiment of the present invention, a wireless communication system is provided that includes an estimation device that can suppress the discrepancy caused by the lag between the estimated time of the propagation path between the transmitter and receiver and the transmission time.

Furthermore, according to an embodiment of the present invention, a program is provided that causes a computer to suppress possible discrepancies due to lag between the estimated time of the propagation path between the transmitter and receiver and the transmission time.

(Configuration 1)
According to an embodiment of the present invention, an estimation device is an estimation device that estimates a frequency response of a propagation path between a transmitter and a receiver in a wireless communication space in which a transmitter having M _T (M _T is an integer of 2 or more) antennas, an IRS that is an electromagnetic wave reflector having _N (N is an integer of 2 or more) reflecting elements whose reflection characteristics can be dynamically changed, and a receiver having M _R (M R is an integer of 2 or more) antennas are non-linearly arranged, when the transmitter transmits a pilot signal that is a known signal to the receiver, and the estimation device comprises an estimation means and an optimization means. Upon receiving a received signal of the pilot signal, the estimation means estimates a frequency response FQR_0 of the propagation path at the time the received signal was received based on the received signal, and then performs an estimation process using an autoregressive model based on the estimated frequency response FQR_0 to estimate G frequency responses FQR_1 to FQR_G that are frequency responses at G (G is an integer greater than or equal to 1 and is the total number of times at which the frequency responses of the propagation path are estimated) time points in the future from the time the receiver received the received signal. The optimization means performs an optimization process using frequency response FQR_0 and the G frequency responses FQR_1 to FQR_G to optimize the reflection coefficients of the N reflecting elements and the transmission weights of the M _T antennas.

(Configuration 2)
In configuration 1, in the estimation process, the estimation means sets the estimated frequency response FQR_0 as the initial value of the frequency response, and estimates the first frequency response FQR_1 from the initial value. Then, the estimation process is executed sequentially for all of g=1 to (G−1) to estimate G frequency responses FQR_1 to FQR_G, estimating g (g is an integer satisfying 1≦g≦(G−1)) frequency responses FQR_g to (g+1) frequency responses FQR_g+1.

(Configuration 3)
In configuration 2, the frequency response FQR_0 and each of the g frequency responses FQR_1 to FQR_g consist of a first frequency response that indicates the frequency response of a direct link, which is the propagation path when radio waves reach the receiver directly from the transmitter, and a second frequency response that indicates the frequency response of an indirect link, which is the propagation path when radio waves reach the receiver from the transmitter via an IRS, and each of the first frequency response and the second frequency response of the frequency response FQR_0 is set to an initial value. Then, in the estimation process, the estimation means estimates a first first frequency response from the initial value of the first frequency response of the estimated frequency response FQR_0 and estimates a first second frequency response from the initial value of the second frequency response of the estimated frequency response FQR_0, then estimates a (g+1)th first frequency response from the gth first frequency response, estimates a (g+1)th second frequency response from the gth second frequency response, estimates a gth frequency response FQR_g consisting of the gth first frequency response and the gth second frequency response, and estimates a (g+1)th frequency response FQR_g+1 consisting of the (g+1)th first frequency response and the (g+1)th second frequency response, thereby estimating G frequency responses FQR_1 to FQR_G.

(Configuration 4)
In any of configurations 1 to 3, when the transmitter sequentially transmits (N+1)M _T pilot signals to the receiver by index modulation in which pilot signals are assigned to antenna patterns of the M T antennas, where only one antenna out of the M _T antennas is used for transmitting the pilot signal and antennas other than the one _antenna are not used for transmitting the pilot signal, the estimation means estimates a frequency response matrix by performing a process of estimating one column of a frequency response matrix indicating the frequency response of a propagation path for all columns of the frequency response matrix, each time one pilot signal is received, and estimates a frequency response FQR_0 consisting of the estimated frequency response matrix.

(Configuration 5)
In configuration 4, transmission of (N+1)MT _pilot signals by index modulation is performed by the transmitter sequentially changing the antenna patterns of the _MT antennas in the index modulation to (N+1) _MT antenna patterns and sequentially transmitting the (N+1) _MT pilot signals.

(Configuration 6)
In the configuration 4 or 5, the estimation means performs matrix interpolation on the estimated frequency response matrix in the estimation process to interpolate between elements of the frequency response matrix, and estimates the frequency response matrix after matrix interpolation as the frequency response FQR_0.

(Configuration 7)
In configuration 6, the estimation means generates a Hankel matrix from the estimated frequency response matrix in the estimation process, decomposes the generated Hankel matrix into a product of first and second matrices by singular value decomposition, and performs updating of the first matrix, updating of the second matrix, and updating of the Hankel matrix a predetermined number of times, thereby performing matrix interpolation.

(Configuration 8)
In any of the configurations 1 to 7, the N reflecting elements are classified into c (c is an integer equal to or greater than 1) clusters, each of which has the same frequency response of the propagation path. The reflecting elements included in each of the c clusters are controlled to have the same reflection characteristics.

(Configuration 9)
In any of configurations 1 to 8, the estimation apparatus further comprises a feedback means for feeding back the reflection coefficients of the N reflecting elements and the transmission weights of the M _T antennas optimized by the optimization means to the IRS and the transmitter, respectively.

(Configuration 10)
According to an embodiment of the present invention, a wireless communication system includes a receiver including the estimation device according to any one of configurations 1 to 9, a transmitter, and an IRS.

(Configuration 11)
Furthermore, according to an embodiment of the present invention, the program is a _program for causing a computer to execute, in an estimation device of a receiver, estimation of a frequency response of a propagation path between a transmitter and a receiver when the _transmitter transmits a pilot signal that is a known signal to the receiver in a wireless communication space in which a transmitter having M _T (M _T is an integer of 2 or more) antennas, an IRS that is an electromagnetic wave reflector having N (N is an integer of 2 or more) reflecting elements whose reflection characteristics can be dynamically changed, and a receiver having M R (M R is an integer of 2 or more) antennas are non-linearly arranged,
a first step of executing an estimation process in which, when an estimation means receives a received signal of a pilot signal, it estimates a frequency response FQR_0 of the propagation path at the time the received signal is received based on the received signal, and, based on the estimated frequency response FQR_0, it uses an autoregressive model to estimate G frequency responses FQR_1 to FQR_G which are frequency responses at G time points (G is an integer equal to or greater than 1 and is the total number of time points at which the frequency responses of the propagation path are estimated) that are future time points from the time the receiver receives the received signal;
a second step in which the optimization means performs an optimization process to optimize the reflection coefficients of the N reflecting elements and the transmission weights of the M _T antennas using the frequency response FQR_0 and G frequency responses FQR_1 to FQR_G.

(Configuration 12)
In configuration 11, in the estimation process of the first step, the estimation means sets the estimated frequency response FQR_0 as the initial value of the frequency response, and estimates the first frequency response FQR_1 from the initial value. Then, the estimation process of estimating the gth (g is an integer satisfying 1≦g≦(G−1)) frequency response FQR_g to the (g+1)th frequency response FQR_g+1 is sequentially executed for all g=1 to (G−1), thereby estimating G frequency responses FQR_1 to FQR_G.

(Configuration 13)
In configuration 12), the frequency response FQR_0 and each of the g frequency responses FQR_1 to FQR_g consist of a first frequency response indicating the frequency response of a direct link, which is a propagation path when radio waves reach the receiver directly from the transmitter, and a second frequency response indicating the frequency response of an indirect link, which is a propagation path when radio waves reach the receiver from the transmitter via an IRS, and each of the first frequency response and the second frequency response of the frequency response FQR_0 is set to an initial value. In the estimation process of the first step, the estimation means estimates a first first frequency response from an initial value of the first frequency response of the estimated frequency response FQR_0 and estimates a first second frequency response from an initial value of the second frequency response of the estimated frequency response FQR_0, then estimates a (g+1)th first frequency response from the gth first frequency response, estimates a (g+1)th second frequency response from the gth second frequency response, estimates a gth frequency response FQR_g consisting of the gth first frequency response and the gth second frequency response, and estimates a (g+1)th frequency response FQR_g+1 consisting of the (g+1)th first frequency response and the (g+1)th second frequency response, and estimates G frequency responses FQR_1 to FQR_G by sequentially executing this process for all g=1 to (G−1).

(Configuration 14)
In any of configurations 11 to 13, when the transmitter sequentially transmits (N+1)M _{T pilot signals to the receiver by index modulation in which pilot signals are assigned to antenna patterns of the M T} antennas, where only one antenna out of the M _T antennas is used for transmitting the pilot signal and antennas other than the one _antenna are not used for transmitting the pilot signal, the estimation means estimates a frequency response matrix by executing a process of estimating one column of a frequency response matrix indicating the frequency response of a propagation path for all columns of the frequency response matrix, each time one pilot signal is received, and estimates a frequency response FQR_0 consisting of the estimated frequency response matrix, in the estimation process of the first step.

(Configuration 15)
In configuration 14, transmission of (N+1)MT _pilot signals by index modulation is performed by the transmitter sequentially changing the antenna patterns of the _MT antennas in the index modulation to (N+1) _MT antenna patterns and sequentially transmitting the (N+1) _MT pilot signals.

(Configuration 16)
In configuration 14 or 15, the estimation means performs matrix interpolation on the estimated frequency response matrix in the estimation process of the first step, interpolating between elements of the frequency response matrix, and estimates the frequency response matrix after matrix interpolation as the frequency response FQR_0.

(Configuration 17)
In configuration 16, the estimation means generates a Hankel matrix from the estimated frequency response matrix in the first step of estimation processing, decomposes the generated Hankel matrix into a product of a first and a second matrix by singular value decomposition, and performs updating of the first matrix, updating of the second matrix, and updating of the Hankel matrix a predetermined number of times, thereby performing matrix interpolation.

(Configuration 18)
In any of configurations 11 to 17, the N reflecting elements are grouped into c (c is an integer equal to or greater than 1) clusters, each of which has the same frequency response of the propagation path. The reflecting elements included in each of the c clusters are controlled to have the same reflection characteristics.

(Configuration 19)
In any of configurations 11 to 18, the program further causes the computer to execute a third step in which a feedback means feeds back the reflection coefficients of the N reflecting elements and the transmission weights of the M _T antennas optimized by the optimization means to the IRS and the transmitter, respectively.

This can suppress the discrepancy caused by the lag between the estimated time of the propagation path between the transmitter and receiver and the transmission time.

1 is a schematic diagram of a wireless communication system according to embodiment 1 of the present invention; FIG. 2 is a schematic diagram of the receiver shown in FIG. 1; FIG. 1 is a conceptual diagram illustrating transmission of a pilot signal. 10 is a timing chart showing the operations of the transmitter 1, the IRS 2, and the receiver 3 when estimating the frequency response of the propagation path. FIG. 10 is a diagram for explaining the effect of performing eigenvalue decomposition on a channel matrix. 3 is a flowchart illustrating the operation of the estimation device shown in FIG. 2 . 7 is a flowchart for explaining the detailed operation of step S6 in FIG. 6. 7 is a flowchart for explaining the detailed operation of step S8 in FIG. 6. 8 is a flowchart for explaining the detailed operation of step S11 in FIG. 7. 10 is a diagram illustrating a comparison between the relationship between the conventional estimated time and the current time and the relationship between the estimated time and the current time according to the first embodiment. FIG. FIG. 10 is a schematic diagram of a wireless communication system according to a second embodiment. FIG. 12 is a schematic diagram of the receiver shown in FIG. 11. FIG. 1 is a conceptual diagram showing a matrix representation of a received signal, a frequency response, a transmitted signal, and white noise. 10A and 10B are conceptual diagrams showing the state of a matrix when a reflective element is switched on and off. FIG. 10 is a conceptual diagram showing the transition of matrices H(t) and g(t) during the training period. FIG. 1 is a conceptual diagram showing components of a matrix g(t). FIG. 16 is a diagram for explaining a problem that occurs when estimating a matrix H(t) of a frequency response of a propagation path by the method shown in FIG. 15 . FIG. 10 is a diagram for explaining a method for extracting elements of an estimated matrix H(t). FIG. 1 is a conceptual diagram illustrating matrix decomposition. FIG. 1 illustrates an optimization algorithm. FIG. 10 is a diagram illustrating a selection matrix. FIG. 10 is a diagram for explaining a method for restoring a time series from an interpolated Hankel matrix R. 13 is a flowchart illustrating the operation of the estimation device shown in FIG. 12 . 24 is a flowchart for explaining the detailed operation of step S21 in FIG. 23. 24 is a flowchart for explaining the detailed operation of step S23 in FIG. 23.

Embodiments of the present invention will be described in detail with reference to the drawings. Note that identical or corresponding parts in the drawings will be designated by the same reference numerals, and their description will not be repeated.

[First Embodiment]
Fig. 1 is a schematic diagram of a wireless communication system according to embodiment 1 of the present invention. Referring to Fig. 1, a wireless communication system 10 according to embodiment 1 of the present invention includes a transmitter 1, an IRS 2, and a receiver 3. The receiver 3 includes an estimation device 4.

Transmitter 1, IRS 2, and receiver 3 are arranged in a wireless communication space. Transmitter 1, IRS 2, and receiver 3 are arranged in a position where the arrangement [Transmitter 1 - IRS 2 - Receiver 3] is not on a straight line. More specifically, if the line connecting Transmitter 1 and IRS 2 is L1 and the line connecting IRS 2 and receiver 3 is L2, Transmitter 1, IRS 2, and receiver 3 are arranged so that the angle α formed by lines L1 and L2 is greater than 0. In other words, Transmitter 1, IRS 2, and receiver 3 are arranged non-linearly in the wireless communication space.

The transmitter 1 has M _T (M _T is an integer equal to or greater than 2) antennas, and the receiver 3 has M _R (M _R is an integer equal to or greater than 2) antennas. M _T may be the same as or different _from M _R.

As such, since the transmitter 1 and receiver 3 have multiple antennas, the wireless communication system 10 transmits and receives signals using MIMO (multiple-input and multiple-output) transmission.

The IRS 2 includes N (N is an integer greater than or equal to 2) reflective elements 21 and an IRS controller 22. The N reflective elements 21 are arranged, for example, in a grid pattern. In other words, the N reflective elements 21 are arranged at equal intervals.

The transmitter 1 transmits a signal using M _T antennas. In the IRS 2, the IRS controller 22 controls the reflection coefficients of the N reflecting elements 21 to control the reflection angle and phase of the radio waves by the N reflecting elements 21. The N reflecting elements 21 then reflect the radio waves incident from the transmitter 1 toward the receiver 3. As a result, the radio waves reflected by the N reflecting elements 21 reach the receiver 3.

Receiver 3 receives radio waves transmitted from transmitter 1. In wireless communication system 10, the propagation path between transmitter 1 and receiver 3 consists of a direct link, in which radio waves from transmitter 1 reach receiver 3 directly, and an indirect link, in which radio waves from transmitter 1 reach receiver 3 via IRS 2.

If there is no obstacle OBT between transmitter 1 and receiver 3, receiver 3 receives radio waves transmitted from transmitter 1 using a direct link and an indirect link.

On the other hand, if an obstacle OBT exists between transmitter 1 and receiver 3, receiver 3 receives the radio waves transmitted from transmitter 1 using an indirect link.

Therefore, in the wireless communication system 10, even if an obstacle OBT exists between the transmitter 1 and the receiver 3, radio waves can be transmitted from the transmitter 1 to the receiver 3 by passing through the IRS 2.

In this embodiment of the invention, we assume the use of IRS in high frequency bands and perform OFDM (Orthogonal Frequency Division Multiplexing) transmission, which is robust against frequency selective fading.

In a wireless communication system 10, when estimating the propagation path from the transmitter 1 to the receiver 3, the transmitter 1 transmits a pilot signal, which is a known signal, via OFDM transmission.

Then, receiver 3 receives the pilot signal transmitted from transmitter 1 and detects the received signal y(t) of that pilot signal.

When the receiver 3 detects the received signal y(t) of the pilot signal, an estimation device 4 in the receiver 3 estimates the frequency response FQR_0 of the propagation path between the transmitter 1 and the receiver 3 at the time _t0 when the receiver 3 receives the received signal y(t) based on the received signal y(t) using a method described below.

Then, using the estimated frequency response FQR_0, the estimation device 4 estimates G frequency responses FQR_1 to FQR_G of the propagation path at G future points in time from point in time _t0 to point in time tG (G is an integer equal to or greater than ₁ and is the total number of points in time at which the frequency responses of the propagation path are to be estimated) by a method described _below .

Thereafter, using the estimated frequency response FQR_0 and the G frequency responses FQR_1 to FQR_G, the estimation device 4 optimizes the N reflection coefficients θ of the N reflecting elements 21 and the transmission weights W of the M _T antennas of the transmitter 1 at times t ₀ to t _G by a method described below. Then, using the communication function of the receiver 3, the estimation device 4 feeds back the optimized N reflection coefficients θ of the N reflecting elements 21 to the IRS controller 22 of the IRS 2, and also feeds back the transmission weights W of the M _T antennas to the transmitter 1.

The transmitter 1 receives the transmission weights W for the M _T antennas from the estimation device 4, and transmits signals by MIMO transmission using the received transmission weights W for the M _T antennas.

The IRS controller 22 receives the N reflection coefficients θ of the N reflecting elements 21 from the estimation device 4, and controls the N reflection coefficients of the N reflecting elements 21 based on the received N reflection coefficients θ of the N reflecting elements 21 to control the reflection angle and phase of the radio waves by the N reflecting elements 21.

Figure 2 is a schematic diagram of the receiver 3 shown in Figure 1. Referring to Figure 2, the receiver 3 includes an antenna 31, communication means 32, and an estimation device 4. The estimation device 4 includes estimation means 41 and optimization means 42.

The antenna 31 consists of M _R antennas. The communication means 32 receives a received signal y(t) of a pilot signal via the antenna 31 and outputs the received signal y(t) of the pilot signal to the estimation means 41 of the estimation device 4.

The communication means 32 receives the reflection coefficients RLT_0 to RLT_G of the N reflecting elements 21 optimized at times t ₀ to t _G and the transmission weights W_0 to W_G of the M _T antennas of the transmitter 1 from the optimization means 42 of the estimation device 4. Then, the communication means 32 transmits the transmission weights W_0 to W_G of the M _T antennas to the transmitter 1 via the antenna 31, and transmits the reflection coefficients RLT_0 to RLT_G of the N reflecting elements 21 to the IRS controller 22.

The estimation means 41 receives a received pilot signal y(t) from the communication means 32, estimates a frequency response FQR_0 at time _t0 based on the received pilot signal y(t) by a method described later, and uses the estimated frequency response FQR_0 to estimate G frequency responses FQR_1 to FQR_G at times _t1 to _tG . The estimation means 41 then outputs the estimated frequency response FQR_0 and the G frequency responses FQR_1 to FQR_G to the optimization means 42.

The optimization means 42 receives the frequency response FQR_0 and the G frequency responses FQR_1 to FQR_G from the estimation means 41, and uses the received frequency response FQR_0 and the G frequency responses FQR_1 to FQR_G to optimize the N reflection coefficients θ of the N reflecting elements 21 and the transmission weights W of the M _T antennas of the transmitter 1 at times t ₀ , t ₁ to t _G by a method described later. The optimization means 42 then outputs the optimized reflection coefficients RLT_0, RLT_1 to RLT_G of the N reflecting elements 21 and the transmission weights W_0, W_1 to W_G of the M _T antennas to the communication means 32.

3 is a conceptual diagram of transmitting pilot signals. Referring to FIG. 3, a transmitter 1 transmits (M _T ×M _R ) pilot signals, which is the number of combinations of M _T antennas at the transmitter 1 and M _R antennas at the receiver 3, by OFDM transmission. In this case, each of the (M _T ×M _R ) pilot signals is modulated by OFDM modulation.

Figure 4 is a timing chart showing the operation of transmitter 1, IRS 2, and receiver 3 when estimating the frequency response of the propagation path.

4, the transmitter 1 notifies the IRS 2 of the transmission of a pilot signal. Then, the transmitter 1 sequentially transmits pilot signals x(1), x(1), ..., x(M _T ) in a period PD_1.

After the period PD_1, the transmitter 1 sequentially transmits pilot signals x(1), x(1), ..., x(M _T ) in each of the periods PD_2 to PD_M _R. In this way, the transmitter 1 transmits (M _T ×M _R ) pilot signals.

When pilot signals x(1), x(1), ..., x(M _T ) are transmitted sequentially during period PD_1, IRS2 sets the modes of the N reflection coefficients of the N reflecting elements 21 to mode Ω(1), and when pilot signals x(1), x(1), ..., x(M _T ) are transmitted sequentially during each of periods PD_2 to PD_M _R , IRS2 sets the modes of the N reflection coefficients of the N reflecting elements 21 to modes Ω(2) to Ω(N+1), respectively.

When receiver 3 detects (M _T ×M _R ) received signals y(t) of (M _T ×M _R ) pilot signals transmitted during periods PD_1 to PD_M _R , estimation device 4 in receiver 3 estimates frequency response FQR_0 at time point t ₀ based on the (M _T ×M _R ) received signals y(t) by a method described later, and uses the estimated frequency response FQR_0 to estimate G frequency responses FQR_1 to FQR_G at G times t ₁ to _tG , thereby completing estimation of frequency responses H ^D and D ^C. Note that frequency response H ^D is the frequency response of the direct link between transmitter 1 and receiver 3, and frequency response H ^C is the frequency response of the indirect link between transmitter 1 and receiver 3.

In an embodiment of the present invention, specific examples of the number of antennas, OFDM symbol length, and number of reflecting elements of transmitter 1 during the training period for estimating the frequency response of the propagation path between transmitter 1 and receiver 3, when the wireless communication system is IEEE802.11n (Wi-Fi), are, for example, the number of antennas (maximum) of transmitter 1 = 4, OFDM symbol length (bandwidth: 20 MHz) = 4 μs, and the number of reflecting elements = 100, respectively.

In embodiment 1, we will explain a method for estimating the frequency response of the propagation path between transmitter 1 and receiver 3.

[Estimation of the frequency response of the propagation path at the time _t0 when the received signal y(t) is received]
Assuming that there is no variation in the propagation path while observing the received signal y(t) (assuming that the frequency response H does not have (t)), and since beamforming is not performed in the transmitter 1, if the transmission weight W in the transmitter 1 is omitted, the received signal y(t) can be expressed by the following equation.

In equation (1), Θ is a matrix representing the N reflection coefficients of the N reflecting elements 21, and n(t) represents additive complex white noise.

When M _T received signals y(t) are observed and the M _T observed received signals y(t) are arranged, the following equation is obtained.

Then, in equation (2), if we multiply Y(t) by the inverse matrix of X(t) from the right, we obtain the following equation:

In the last line of equation (3), H consists of [H ^D H ^C ], which includes the frequency response H ^D in the direct link and the frequency response H ^C in the indirect link, and Ω consists of a matrix in which an identity matrix I and Θ (the reflection coefficient matrix of N reflecting elements 21) are arranged vertically.

Then, when the modes of the N reflecting elements 21 are switched (i.e., when the patterns of the N reflection coefficients of the N reflecting elements 21 are switched), the following equation is obtained:

However, in equation (4), the relationship t = _iMT is satisfied. As a result, t represents the timing at which x(1) to x( _MT ) are transmitted in each of the periods PD_1 to _{PD_MR} shown in Fig. 4, and "i" in t = _iMT represents Ω(1) to Ω(N+1) shown in Fig. 4.

By observing N+1 G(i)s in equation (4) and arranging the N G(i)s, we obtain the following equation.

Then, if we multiply g in equation (5) by the inverse matrix of R on the right, we get the following equation:

According to equation (5), R consists of [Ω(1)...Ω(N+1)], which is known because it consists of N+1 modes of reflection coefficients (i.e., patterns of N+1 reflection coefficients) of N reflecting elements 21. Therefore, the inverse matrix of R can be calculated.

Furthermore, g in equation (6) can be calculated using G(t) = Y(t)X ^-1 (t) in equation (3), where Y(t) is known because it is the signal received when the receiver 3 receives the pilot signal, and X(t) is known because it is the signal transmitted by the transmitter 1. As a result, "gR ^-1 " in equation (6) can be calculated.

Furthermore, in the embodiment of the present invention, it is assumed that "the amount of fluctuation in the propagation path is sufficiently larger than the noise power (the signal-to-noise ratio SN is high)." In this case, "N" in equation (6) can be ignored, and H ^D and H ^C in equation (6) can be estimated with high accuracy by setting H ^D ≒ [H ^D ]^ (the hat of H ^{D )} and H ^C ≒ [H ^{C ]} ^ (the hat of ^HC ), respectively. Therefore, hereinafter, the estimated value of the frequency response H will also be represented as "H."

In this way, since "N" in equation (6) can be ignored, by calculating gR ^-1 and NR ^-1 , the frequency responses H ^D and H ^C can be independently determined using equation (6). The frequency response H ^D is the frequency response of the direct link between the transmitter 1 and the receiver 3, and the frequency response H ^C is the frequency response of the indirect link between the transmitter 1 and the receiver 3.

As a result, using the above-mentioned equations (1) to (6), it is possible to estimate the frequency response [H ^D H ^C ] (=FQR_0) of the propagation path between the transmitter 1 and the receiver 3 at the time t ₀ when the received signal y(t) is received.

When the estimation means 41 of the estimation device 4 receives the received signal y(t), it estimates the frequency response [H ^D H ^C ] of the propagation path at the time of reception t ₀ based on the received signal y(t) using equations (1) to (6).

[Estimation of the frequency response of the propagation path from the reception time _t0 to a future time point]
If the transmission symbol of the k-th subcarrier transmitted from all of the M _T antennas is x(k)εC ^M T , the received signal y(k) is expressed by the following equation.

In equation (7), the total number of subcarriers k is K. The delay due to the propagation path is assumed not to exceed the guard interval. Furthermore, H(k)∈C ^MR×MT is a propagation path matrix representing the frequency response of the kth subcarrier, where the rows and columns correspond to the receiving antenna and the transmitting antenna, respectively. Furthermore, n(k) represents additive complex white noise with a mean of 0 and a variance of σ ² .

The elements of the propagation path matrix shown in equation (7) can be decomposed into the direct link component that reaches receiver 3 directly from transmitter 1 and the indirect link component that passes through IRS 2, as shown in the following equation:

In equation (8), the first term on the right-hand side corresponds to the direct link, and the second term corresponds to the indirect link via IRS2.

Then, h ^D _mR,mT (k) represents the frequency response of the kth subcarrier from the mth _T transmitting antenna to the mth _R receiving antenna, h ^IU _mR,n (k) represents the frequency response of the kth subcarrier from the nth element of IRS2 to the mth _R receiving antenna, and h ^BI _n,mT (k) represents the frequency response of the kth subcarrier from the mth _T transmitting antenna to the nth element of IRS2.

Furthermore, θ _n represents the reflection coefficient at the nth element of IRS 2. Furthermore, these are collected in vector form and defined as h ^IU _mR (k) = [h ^IU _mR,1 (k), ..., h ^IU _mR,N (k)] ^T , h ^BI _mT (k) = [h ^BI _1,mT (k), ..., h ^BI _N,mT (k)] ^T , θ = [θ ₁ , ..., θ _N ] ^T. In this definition, "T" represents transpose.

Furthermore, the channel in which the channels from transmitter 1 to IRS 2 and from IRS 2 to receiver 3 are superimposed is called a cascaded channel, and its frequency response is obtained as the Hadamard product of h ^IU _mR (k) and h ^BI _mT (k) as shown in equation (9).

Substituting equation (8) into equation (7) gives the following equation:

H ^D (k) in equation (10) is expressed by the following equation.

Furthermore, H ^C (k) in equation (10) is expressed by the following equation.

Furthermore, Θ in equation (10) is expressed by the following equation:

In this embodiment of the present invention, it is assumed that the frequency response of a propagation path can be expressed as a linear combination of P past data (P is an integer equal to or greater than 1) (Non-Patent Document 7). Therefore, the time series of the frequency response matrix of the frequency response of the propagation path is expressed as an AR model (autoregressive model), i.e., an autoregressive model, as shown in the following equation.

Note that the following will only describe the cascade channel (the frequency response of the propagation path from transmitter 1 to receiver 3 via IRS 2), but the same applies to the direct link from transmitter 1 to receiver 3.

In equation (14), h ^C _mR,mT,n (k, t) is the n-th element of the cascaded channel h ^C _mR,mT (k), P is the AR order, t is an index representing time, and ε(t) is a noise term representing the error in fitting the AR model.

By calculating the AR coefficient (regression coefficient) a _p , it becomes possible to estimate the channel estimation value at a future time (the left side of equation (14)) from the past channel estimation value (the right side of equation (14)). The AR coefficient can be estimated by solving the following Yule-Walker equation.

In equation (15), γ^(p) is the sample autocovariance of h ^C _mR,mT,n (k) and is expressed by the following equation: Note that the notation "γ^(p)" indicates that "^" is placed above γ, as shown in equation (15).

In equation (16), "*" represents a complex conjugate. μ in equation (16) is expressed by the following equation:

In equation (17), T is the number of training samples.

By solving equation (15), the estimated value of the AR coefficient a^ _p is obtained. Note that the notation "a^ _p " indicates that "^" is placed above the a. From this estimated value of the AR coefficient a^ _p and the past channel estimation value, the predicted value of the channel at the current time can be expressed as follows:

Equation (18) represents the predicted channel value at the current time for the cascaded channel, but when equations (14), (16), and (17) for the cascaded channel are expressed for the channel in the direct link, they become equations (19), (20), and (21).

Then, when calculating the AR coefficient a _p for the channel in the direct link, equations (15), (20), and (21) are used.

By finding the AR coefficient a _p , a prediction of the channel at the current time for the direct link can be realized as follows:

Furthermore, when estimating the frequency response of a propagation path at multiple future times (multiple time points), the predicted value obtained by equation (18) for the frequency response of a cascaded channel is substituted for the observed value on the right-hand side of equation (18), and estimation by equation (18) is sequentially calculated, thereby making it possible to estimate the frequency response at any future time (future point in time).

Similarly, for the frequency response of the channel in the direct link, the predicted value obtained by equation (22) is substituted for the observed value on the right-hand side of equation (22), and by sequentially calculating the estimate using equation (22), it is possible to estimate it at any future time (future point in time).

Therefore, by using equations (18) and (22), it is possible to estimate the frequency response of the propagation path (a propagation path consisting of a direct link and an indirect link) between transmitter 1 and receiver 3 at any time in the future.

The estimation means 41 of the estimation device 4 uses equations (7) to (22) to estimate the frequency response of the propagation path (a propagation path consisting of a direct link and an indirect link) between the transmitter 1 and the receiver 3 at any future time.

Optimization of Reflection Coefficients of Reflective Elements and Transmit Weights in Transmitter 1
The optimization of the N reflection coefficients θ of the N reflecting elements 21 and the optimization of the transmission weights W in the transmitter 1 will be described.

The optimization means 42 of the estimation device 4 optimizes the N reflection coefficients θ and transmission weights W through alternating optimization so as to maximize the transmission capacity sum_rate of the signal transmitted by the transmitter 1.

That is, the optimization problem is expressed by the following equation:

In equation (23), γ _mR is the signal to interference and noise ratio (SINR) of the M _R antennas, and is a function of the reflection coefficient θ and the transmission weight W. Also, ω _mR is a parameter representing the priority of each receiving antenna. In particular, if no priority is assigned to the antennas, ω ₁ = ω ₂ = ... = ω _MR = 1/M _R may be used.

Equation (23) represents the determination of the reflection coefficient θ and transmission weight W when the right-hand side is maximized.

The optimization means 42
(I) calculating a propagation path matrix for the reflection coefficient θ _n , and calculating a transmission weight W _n by performing eigenvalue decomposition on the calculated propagation path matrix; and (II) calculating a transmission capacity sum_rate_n using the calculated transmission weight W _n .
This is performed for n=1 to ^QN ,
(III) Determine the reflection coefficient θ _opt and transmission weight W _opt when the maximum transmission capacity sum_rate_max is obtained among the ^QN transmission capacities sum_rate_1 to ^sum_rate_QN , where Q is the number of reflection coefficients that each reflecting element can take.

In (I), the optimization means 42 calculates the channel matrix by calculating [H ^D (k, t) + H ^C (k, t) Θ]W using the frequency responses H ^D (k, t) and H ^C (k, t) received from the estimation means 41. In this case, the frequency responses H ^D (k, t) and H ^C (k, t) have been estimated by the estimation means 41, "Θ" represents the pattern of ^QN reflection coefficients of the N reflecting elements 21, and the optimization means 42 shares in advance with the IRS 2 a codebook including ^QN patterns as the patterns of the ^QN reflection coefficients of the N reflecting elements 21, so the optimization means 42 can calculate the channel matrix [H ^D (k, t) + H ^C (k, t) Θ]W.

Therefore, the optimization means 42 detects one pattern _θn consisting of N reflection coefficients from the codebook, and substitutes the detected one pattern _θn into “Θ” to calculate the propagation path matrix [H ^D (k, t) + H ^C (k, t) Θ]W.

Then, the optimization means 42 calculates the transmission weights W by performing eigenvalue decomposition on the calculated channel matrix [H ^D (k, t) + H ^C (k, t) Θ]W.

In (II), the optimization means 42 multiplies the M _R transmission rates for the M _R antennas by the priority ω _mR using the transmission weights W calculated in (I), and calculates the sum of the M _R multiplication results to calculate the transmission capacity sum_rate. The M _R transmission rates for the M _R antennas are calculated as log ₂ (1 + γ _mR ) in equation (23). How to calculate "γ _mR " will be described later.

Furthermore, in (III), if there are a plurality of maximum transmission capacities sum_rate_max, the optimization means 42 extracts any one of the plurality of maximum transmission capacities sum_rate_max and determines the reflection coefficient θ _opt and the transmission weight W _opt .

In (I), we explain the effect of performing eigenvalue decomposition on the channel matrix.

Figure 5 is a diagram illustrating the effect of performing eigenvalue decomposition on the channel matrix.

The transmitter 1 multiplies (precodes) the transmission signal of each antenna by a coefficient matrix based on the propagation path matrix information obtained from the estimation device 4, so that the propagation paths of the antenna pairs are independent.

Therefore, transmitter 1 determines the coefficient matrix using the following equation:

In equation (24), matrix T is a transmission weight matrix, which corresponds to the above-mentioned transmission weight W. Furthermore, matrix A is a K×K diagonal matrix, where K is the number of streams, and p ₁ , ..., p _K are transmission powers allocated to streams 1 to K, respectively.

When the transmitted signal s is multiplied by matrices T and A, the received signal y is expressed by the following equation:

Multiplying the received signal y by T ^H H ^H gives the following equation:

ΧA in the last line of equation (26) is a diagonal matrix. The results of dividing each diagonal element (M _R ) of ΨA by the noise power (or an estimated value of noise power) of each antenna become γ ₁ , γ ₂ , ..., γ _MR in equation (23). Therefore, the results of dividing each diagonal element (M _R ) of ΨA by the noise power (or an estimated value of noise power) of each antenna are substituted for γ _mR in equation (23) to calculate the M _R transmission rates for the M _R antennas, and the calculated M _R transmission rates for the M _R antennas are used to calculate the transmission capacity sum_rate.

Referring to Figure 5, when precoding is not performed, a communication path is formed between each transmitting antenna and receiving antenna in which communication paths from multiple transmitting antennas are superimposed (see (a) of Figure 5).

On the other hand, when precoding is used, multiple independent communication paths can be formed between the transmitting antenna and the receiving antenna (see (b) in Figure 5).

As a result, by performing eigenvalue decomposition on the channel matrix, in the above (II), the optimization means 42 multiplies the M _R transmission rates for the M _R antennas by the priority ω _mR using the transmission weights W calculated in (I), and calculates the sum of the M _R multiplication results, thereby being able to calculate the transmission capacity sum_rate reaching the antenna of the receiver 3.

In other words, for one receiving antenna, one transmission capacity for one communication path is calculated, and the calculation results are added up for the number of receiving antennas to calculate the transmission capacity sum_rate. As a result, the amount of calculation required to calculate the transmission capacity sum_rate can be reduced.

Figure 6 is a flowchart illustrating the operation of the estimation device 4 shown in Figure 2. Referring to Figure 6, when the operation of the estimation device 4 begins, the estimation means 41 of the estimation device 4 receives the received signal y(t) of the pilot signal from the communication means 32 of the receiver 3 (step S1).

The estimation means 41 then derives equation (6) using equations (1) to (5) based on the received signal y(t) (step S2).

Thereafter, the estimation means 41 calculates the frequency responses H ^D and H ^C of the propagation path using equation (6) to estimate the frequency response FQR_0 of the propagation path at the time t ₀ when the received signal y(t) is received (step S3).

Subsequently, the estimation means 41 calculates the AR coefficient a _{p_C} using equations (15) to (17) (step S4).

Then, the estimation means 41 calculates the AR coefficient a _{p_D} using equations (15), (20) and (21) (step S5).

Thereafter, the estimation means 41 estimates the frequency response FQR_1 from the frequency response FQR_0 using the AR coefficients a _{p_C} and a _{p_D} according to the equations (18) and (22) (step S6).

Then, the estimation means 41 sets g=1 (step S7), and estimates the frequency response FQR_g+1 at a time _{tg +1} that is later than the time _tg from the frequency response FQR_g at the time _tg using the AR coefficients _{ap_C} and ap_D (step S8).

The estimation means 41 then determines whether g = G-1 (step S9).

If it is determined in step S9 that g is not equal to G-1, the estimation means 41 sets g to g+1 (step S10). The operation of the estimation device 4 then proceeds to step S8, and steps S8 to S10 are repeatedly executed until it is determined in step S9 that g is equal to G-1.

Then, in step S9, if it is determined that g = G-1, the estimation means 41 outputs the frequency responses FQR_0 to FQR_G to the optimization means 42.

The optimization means 42 receives the frequency responses FQR_0 to FQR_G from the estimation means 41 and optimizes the reflection coefficient Θ and transmission weight W based on the received frequency responses FQR_0 to FQR_G (step S11).

Then, the optimization means 42 feeds back the optimized reflection coefficient Θ to the IRS 2 and the optimized transmission weight W to the transmitter 1 via the communication means 32 of the receiver 3 (step S12). This completes the operation of the estimation device 4.

In the flowchart shown in FIG. 6, when step S8 is executed for the first time, the estimation means 41 uses the AR coefficients a _{p_C} and a _{p_D} to estimate the frequency response FQR_2 from the frequency response FQR_1 estimated in step S6 according to equations (18) and (22).

Then, when step S8 is executed for the second time, the estimation means 41 estimates the frequency response FQR_3 from the frequency response FQR_2 by using the AR coefficients a _{p_C} and a _{p_D} according to equations (18) and (22).

Next, when step S8 is executed for the third time, the estimation means 41 estimates the frequency response FQR_4 from the frequency response FQR_3 by using the AR coefficients a _{p_C} and a _{p_D} according to equations (18) and (22).

Thereafter, in the same manner, when step S8 is executed for the (G-2)th time, the estimation means 41 uses the AR coefficients a _{p _C} and a _{p _D} to estimate the frequency response FQR_G-1 from the frequency response FQR_G-2 according to equations (18) and (22).

Then, when step S8 is executed for the (G-1)th time, the estimation means 41 estimates the frequency response FQR_G from the frequency response FQR_G-1 by using the AR coefficients a _{p_C} and a _{p_D} according to equations (18) and (22).

Therefore, by executing step S8 (G-1) times, frequency responses FQR_2 to FQR_G can be estimated.

As a result, according to the flowchart shown in FIG. 6, it is possible to estimate the frequency response FQR_0 at the time _t0 of reception of the received signal y( _t ) (see step S3) and the frequency responses FQR_1 to FQR_G at times _t1 to _tG in the future from the time t0 of reception (see steps S6, S8 to S10).

Fig. 7 is a flowchart for explaining the detailed operation of step S6 in Fig. 6. Referring to Fig. 7, after step S5 in Fig. 6, the estimation means 41 estimates the frequency response H ^C 1 at a time point t ₁ that is later than the reception time t ₀ by substituting the frequency response H ^C ₀ and the AR coefficient a _{p_C} of the frequency response _{FQR_0} into the right side of equation (18) using equation (18) (step S61).

Then, the estimation means 41 substitutes the frequency response H ^D ₀ of the frequency response FQR_0 and the AR coefficient a _{p — D} into the right side of equation (22) to estimate the frequency response H ^D ₁ at a time t ₁ that is later than the reception time t ₀ using equation (22) (step S62).

Thereafter, the estimation means 41 generates a frequency response FQR_1 at the time _{t1 that} is composed of the frequency response H ^C1 _and the frequency response H ^D1 (step S63). Thereafter, the operation of the estimation device 4 proceeds to step S7 in FIG.

In this way, the estimation means 41 estimates the frequency responses H ^C ₁ and H ^D ₁ from the frequency responses H ^C ₀ and H ^D ₀ for each indirect link and direct link of the propagation path using equations (18) and (22), respectively.

Fig. 8 is a flowchart for explaining the detailed operation of step S8 in Fig. 6. Referring to Fig. 8, after step S7 or step S10 in Fig. 6, the estimation means 41 substitutes the frequency response H ^C _g of the frequency response FQR_g and the AR coefficient a _{p_C} into the right side of equation (18) to estimate a frequency response H ^C _g+1 at a time point t _g+1 that is later than the time point t _g using equation (18) (step S81).

Then, the estimation means 41 substitutes the frequency response H ^D _g of the frequency response FQR_g and the AR coefficient a _{p — D} into the right side of equation (22) to estimate the frequency response H ^D _g+1 at a time point t _g+1 that is later than the time point t _g using equation (22) (step S82).

Thereafter, the estimation means 41 generates a frequency response FQR_g+1 at the time t _g+1 , which is composed of the frequency response H ^C _g +1 and the frequency response H ^D _g+1 (step S83). Thereafter, the operation of the estimation device 4 proceeds to step S9 in FIG. 6.

In this way, the estimation means 41 estimates the frequency responses H ^C _{g +1} and H ^D g+1 from the frequency responses H ^C g and H ^D _g by equations (18) and (22), respectively, for each indirect link and _direct link of the propagation path.

Then, when g=1, in step S81, the frequency response H ^C ₂ of the frequency response FQR_2 is estimated from the frequency response H ^C ₁ of the frequency response FQR_1, and in step S82, the frequency response H ^D ₂ of the frequency response FQR_2 is estimated from the frequency response H ^D ₁ of the frequency response FQR_1.

Then, in step S83, a frequency response FQR_2 consisting of the frequency response H ^C ₂ and the frequency response H ^D ₂ is generated.

8, a frequency response FQR_2 consisting of frequency response H ^C ₂ and frequency response H D 2, a frequency response FQR_3 consisting of frequency response H ^C ₃ and frequency response H ^D ₃ , a frequency response FQR_4 consisting of frequency response H ^C ₄ and frequency response H ^D ₄ , _... , a frequency response FQR_G consisting of frequency response ^{H C G} _and frequency response H ^D _G are generated.

Figure 9 is a flowchart for explaining the detailed operation of step S11 in Figure 7. Referring to Figure 9, when it is determined in step S9 in Figure 6 that g = G - 1, the optimization means 42 sets g = 0 (step S111) and n = 1 (step S112).

Then, the optimization means 42 detects the reflection coefficient θ _{n_g} from the stored codebook, and calculates the channel matrix [H ^D (k, t) + H ^C (k, t) Θ] W_n_g for the detected reflection coefficient θ _{n_g} using the frequency responses H ^D (k, t) and H ^C (k, t) estimated by the estimation means 41 (step 113).

Thereafter, the optimization means 42 performs eigenvalue decomposition on the channel matrix [H ^D (k, t)+H ^C (k, t) Θ]W_n_g to calculate transmission weights W _{n_g} (step S114).

Subsequently, the optimization means 42 calculates a transmission capacity sum_rate_n_g using the transmission weight _{Wn_g} (step S115).

Then, the optimization means 42 determines whether n= ^QN (step S116).

If it is determined in step S116 that n is not equal to ^QN , the optimization means 42 sets n to n+1 (step S17). Thereafter, the operation of the estimation device 4 proceeds to step S113, and steps S113 to S117 are repeatedly executed until it is determined in step S116 that n is equal to ^QN .

If it is determined in step 116 that n=Q ^N , the optimization means 42 determines the reflection coefficient θ _{opt_g} and the transmission weight W _{opt_g} when the maximum transmission capacity sum_rate_max_g is obtained among the Q ^N transmission capacities sum_rate_1_g to sum_rate_Q ^N _g (step S118).

The optimization means 42 then determines whether g = G (step S119). If it is determined in step S119 that g = G is not true, the optimization means 42 sets g = g + 1 (step S120). The operation of the estimation device 4 then proceeds to step S112, and steps S112 to S120 are repeatedly executed until it is determined in step S119 that g = G.

If it is determined in step S119 that g=G, the optimization means 42 obtains the reflection coefficients θ _{opt — 0} to θ _{opt — G} and the transmission weights W _{opt — 0} to W _{opt — G} optimized at times t ₀ to t _G (step S121). Thereafter, the operation of the estimation device 4 proceeds to step S12 in FIG. 6.

In step S121, the optimization means 42 obtains the optimized reflection coefficients θ _{opt — 0} to θ _{opt — G} and transmission weights W _{opt — 0} to W _{opt — G.} In step S12 of FIG. 6, the optimization means 42 feeds back the transmission weights W _{opt — 0} to W _{opt — G} to the transmitter 1, respectively corresponding to times t ₀ to t _G , as shown in Table 1, and feeds back the reflection coefficients θ _{opt —} 0 to θ _{opt —} G to the IRS 2, respectively corresponding to times t ₀ to t _G.

According to the flowchart shown in FIG. 6 (including the flowcharts shown in FIGS. 7 to 9 ), the estimation device 4 estimates, based on the received signal y(t), the frequency response FQR_0 of the propagation path at the time t ₀ of reception of the received signal y(t) (see steps S2 and S3), estimates the frequency response FQR_1 of the propagation path at a time t ₁ that is later than the time of reception t ₀ from the frequency response FQR_0 of the propagation path (see step S6), estimates the frequency response FQR_2 of the propagation path from the frequency response FQR_1 of the propagation path, estimates the frequency response FQR_3 of the propagation path from the frequency response FQR_2 of the propagation path, estimates the frequency response FQR_4 of the propagation path from the frequency response FQR_3 of the propagation path, ... and similarly estimates the frequency response FQR_G of the propagation path from the frequency response FQR_G-1 of the propagation path (see steps S8 to S10).

Then, in steps S8 to S10, the estimation device 4 uses the frequency response FQR_1 of the propagation path as an initial value and repeatedly estimates the frequency response FQR_g+1 at time t _{g +1} from the frequency response FQR_g at time t _g of two adjacent times t _{g and t g+1} using equations (18) and (22), thereby estimating the frequency responses FQR_2 to FQR_G at times t ₂ to t _G , respectively.

Therefore, by setting the times t ₁ to t _G to the times of signal transmission, it is possible to suppress the discrepancy due to the lag between the estimated time of the propagation path between the transmitter 1 and the receiver 3 and the transmission time.

According to the flowchart shown in FIG. 6 (including the flowcharts shown in FIGS. 7 to 9), the estimation device 4 optimizes the reflection coefficient Θ and the transmission weight W by adding frequency responses FQR_1 to FQR_G estimated at times _{t 1 to} t _G that are later than the reception time t ₀ to the frequency response FQR_0 at the reception time t 0 estimated based on the received signal y(t).

Then, the estimation device 4 feeds back the optimized transmission weights W _{opt — 0} to W _{opt — G} to the transmitter 1, respectively corresponding to times t ₀ to t _G (see Table 1), and feeds back the optimized reflection coefficients θ _opt — 0 to θ _{opt — G} to the IRS 2, respectively corresponding to times t ₀ to t _G (see Table 2).

Therefore, transmitter 1 transmits a signal using the fed-back transmission weights W _{opt — 0} to W _{opt — G} , and IRS 2 reflects the transmitted signal from transmitter 1 using the fed-back reflection coefficients θ _{opt — 0} to θ _{opt — G} , so that the signal can be transmitted to receiver 3 using a propagation path (frequency response) that suppresses deviation from the estimated path.

Figure 10 shows a comparison between the relationship between the conventional estimated time and the current time and the relationship between the estimated time and the current time in embodiment 1.

Referring to (a) in Figure 10, conventionally, the frequency response of the propagation path was estimated using information up to the estimated time, and the reflection coefficient θ and transmission weight W were optimized using the estimated frequency response. As a result, there was a delay between the estimated time and the current time due to the estimation process, optimization process, and feedback of the optimized reflection coefficient θ and transmission weight W.

On the other hand, in the first embodiment, as shown in (b) of FIG. 10 , the frequency response FQR_0 at the time of reception t ₀ is estimated based on the received signal y(t) at the conventional estimated time, and the estimated frequency response FQR_0 is used to sequentially estimate frequency responses FQR_1 to FQR_G at times t ₁ to t _G that are later than the time of reception t ₀ using equations (18) and (22). In addition, the estimated frequency responses FQR_0 to FQR_G are used to optimize the reflection coefficient θ and the transmission weight W. Therefore, the reflection coefficient θ and the transmission weight W can be optimized using information up to the conventional current time.

As a result, the discrepancy due to the lag between the estimated time of the propagation path between the transmitter and receiver and the transmission time can be suppressed.

In embodiment 1, the operation of the estimation device 4 may be implemented by software. In this case, the estimation device 4 includes a CPU (Central Processing Unit), a ROM (Read Only Memory), and a RAM (Random Access Memory). The ROM stores a program Prog_A consisting of the steps of the flowchart shown in FIG. 6 (including the flowcharts shown in FIGS. 7 to 9).

The CPU reads out the program Prog_A from the ROM and executes the read out program Prog_A to estimate frequency responses FQR_0 to FQR_G from time t ₀ to t _G , and optimizes the transmission weights W and the reflection coefficients θ from time t ₀ to t _G using the frequency responses FQR_0 to FQR_G, and feeds back the optimized transmission weights W and the reflection coefficients θ to the transmitter 1 and the IRS 2. The RAM temporarily stores a codebook including patterns of ^QN reflection coefficients for the N reflecting elements 21.

Furthermore, the program Prog_A may be recorded on a recording medium such as a CD, a DVD, etc. and distributed. When a recording medium on which the program Prog_A is recorded is attached to a computer, the computer reads and executes the program Prog_A from the recording medium to estimate frequency responses FQR_0 to FQR_G from time t ₀ to t _G , and optimizes the transmission weights W and the reflection coefficients θ from time t ₀ to t _G using the frequency responses FQR_0 to FQR_G, and feeds back the optimized transmission weights W and reflection coefficients θ to the transmitter 1 and the IRS 2, respectively.

Therefore, the recording medium on which the program Prog_A is recorded is a computer-readable recording medium.

When transmitter 1 has a small number of antennas, indirect links that pass through several adjacent reflecting elements will have the same propagation path value. Therefore, by classifying reflecting elements with the same propagation path value into clusters and performing the same control on the reflecting elements within each cluster, the overhead of propagation path estimation can be reduced.

When estimating propagation paths in conjunction with clustering, estimation only needs to be performed for the reflecting elements that represent each cluster.

This reduces the amount of calculation required for estimation.

When N reflecting elements 21 are clustered, the N reflecting elements 21 are classified into c clusters (c is an integer greater than or equal to 1), each of which has the same frequency response of the propagation path. Then, c representative reflecting elements are selected from the c clusters. In this case, for example, among the reflecting elements included in one cluster, the reflecting element whose arrangement position is the center of the arrangement positions of the reflecting elements is selected as the representative reflecting element.

The reflective elements contained in each of the c clusters are then controlled to have the same reflective characteristics.

[Embodiment 2]
Fig. 11 is a schematic diagram of a wireless communication system according to embodiment 2. Referring to Fig. 11, wireless communication system 10A according to embodiment 2 is the same as wireless communication system 10, except that IRS 2 of wireless communication system 10 shown in Fig. 1 is changed to IRS 2A and receiver 3 is changed to receiver 3A.

Transmitter 1, IRS 2A, and receiver 3A are arranged in a wireless communication space. Transmitter 1, IRS 2A, and receiver 3A are arranged non-linearly in the wireless communication space, similar to transmitter 1, IRS 2, and receiver 3 in embodiment 1.

The IRS2A is identical to the IRS2, except that the IRS controller 22 of the IRS2 shown in Figure 1 has been replaced with the IRS controller 22A.

Receiver 3A is the same as receiver 3, except that the estimation device 4 of receiver 3 shown in Figure 1 has been replaced with estimation device 4A.

When the estimation device 4A of the receiver 3 estimates the frequency response of the propagation path between the transmitter 1 and the receiver 3A, the IRS controller 22A controls the N reflecting elements 21 so as to sequentially switch the reflection pattern of the N reflecting elements 21 to (N+1)M _T patterns when (N+1)M _T pilot signals are sequentially transmitted from the transmitter 1.

At this time, the IRS controller 22A controls the one reflective element to be turned "ON" in a predetermined order so that only one of the N reflective elements is turned "ON" and the other (N-1) reflective elements are turned "OFF."

When the estimation device 4A of the receiver 3A receives a received signal y(t) of one pilot signal from the communication means 32, it estimates one column CLM_c of a frequency response matrix [H ^D H ^C ] indicating the frequency response of the propagation path, and when it receives a received signal y(t+1) of another pilot signal from the communication means 32, it estimates one column CLM_c+1 adjacent to one column CLM_c in the frequency response matrix [H ^D H ^C ], performing this process for all of the (N+1)M _T pilot signals y(1) to y((N+1)M _T ), thereby estimating the frequency response matrix [H ^D H ^C ].

Then, the estimation device 4A estimates the frequency response matrix [H ^D H ^C ] based on the (N+1)M _T pilot signals y(1) to y((N+1)M _T ), and then interpolates missing elements from the frequency response matrix [H ^D H ^C ] using a method described later, and estimates the complete frequency response matrix [H ^D H ^C ] as the frequency response FQR_0 at time t ₀ .

Thereafter, the estimation device 4A uses the frequency response FQR_0 to sequentially estimate frequency responses FQR_1 to FQR_G at times t ₁ to _tG , in the same way as the estimation device 4 in the first embodiment.

Then, in the same way as the estimation device 4 in embodiment 1, the estimation device 4A optimizes the reflection coefficient θ and transmission weight W using the estimated frequency responses FQR_0 to FQR_G, feeds back the optimized transmission weight W to the transmitter 1, and feeds back the optimized reflection coefficient θ to the IRS 2A.

Figure 12 is a schematic diagram of the receiver 3A shown in Figure 11. Referring to Figure 12, the receiver 3A is the same as the receiver 3 shown in Figure 2, except that the estimation device 4 is replaced with an estimation device 4A.

The estimation device 4A is the same as the estimation device 4, except that the estimation means 41 of the estimation device 4 shown in Figure 2 is replaced with estimation means 41A.

The estimation means 41A estimates the frequency response FQR_0 of the propagation path at the time _t0 of reception of the received signal y(t) by a method described later. Then, the estimation means 41A uses the estimated frequency response FQR_0 to estimate frequency responses FQR_1 to FQR_G at times _t1 to _tG that are later than the time _t0 of reception by the same method as the estimation means 41. Thereafter, the estimation means 41A outputs the estimated frequency responses FQR_0 to FQR_G to the optimization means 42.

[Estimation of the frequency response of the propagation path at the time _t0 when the received signal y(t) is received]
To take into account the fluctuations in the propagation path during the training period, which is the period for estimating the frequency response of the propagation path, and during the data transmission period, we employ estimation by ON/OFF switching of N reflecting elements 21, which can estimate each column of the propagation path matrix H(t) at OFDM symbol intervals (Non-Patent Document 8). When a reflecting element is turned OFF, the reflection coefficient of the turned OFF reflecting element can be set to "0".

Figure 13 is a conceptual diagram showing the matrix representation of the received signal, frequency response, transmitted signal, and white noise.

13, the received signal y(t) is expressed by equation (Eq), where matrix H(t) is a frequency response matrix consisting of the frequency response matrix H ^D (t) of the direct link and the frequency response matrix H ^C (t) of the indirect link, and matrix g(t) is the product of the reflection coefficient matrix Θ and the transmitted signal matrix x(t).

The matrix H(t) is a matrix with M _R rows and (N+1)M _T columns, the matrix g(t) is a matrix with (N+1)M _T rows and 1 column, and the matrix n(t) is a matrix with M _R rows and 1 column.

14 is a conceptual diagram showing the state of the matrix when the reflecting elements are switched ON/OFF. Referring to FIG. 14, when transmitter 1 transmits a pilot signal using one antenna and all N reflecting elements 21 are turned OFF (=0), the elements in the first row of matrix g(t) are "1" (see the hatching in matrix g(t)), and the elements in the second row to the (N+1) _MTth row are "0".

As a result, the received signal y(t) is the sum of a matrix H(t) consisting of the elements in the first column and a matrix n(t) representing white noise. When the signal-to-noise ratio SN is high, the influence of white noise is small and can be ignored. Therefore, when all reflecting elements are turned OFF (=0) and a pilot signal is transmitted from one antenna of transmitter 1, estimation means 41A estimates the elements in the first column of matrix H(t) by receiving received signal y(t) via antenna 31 and communication means 32. Because transmitter 1 transmits a pilot signal using one antenna and IRS 2A reflects the pilot signal with one reflecting element, the path from transmitter 1 to IRS 2 to receiver 3A consists of one path, matrix H(t) consists of one column element, and one column element of matrix H(t) corresponds to one antenna of transmitter 1.

In IRS2A, by switching one reflective element to be ON (=1) in a predetermined order, it is possible to sequentially estimate elements from the second column to the (N+1) _MT column of the matrix H(t).

In embodiment 2, transmitter 1 transmits pilot signals using one antenna at intervals equal to the OFDM symbol length (e.g., 4 μs).

Figure 15 is a conceptual diagram showing the evolution of matrices H(t) and g(t) during the training period.

Referring to FIG. 15, at t=1, when the element in the first row of matrix g(t) becomes “1” (see the hatching in matrix g(t)) and the elements in the second row to the (N+1)M _Tth row of matrix g(t) become “0”, the estimation means 41A estimates the element in the first column of matrix H(t) by receiving a pilot signal transmitted from one antenna of the transmitter 1.

Then, at t=2, when the elements in the second row of matrix g(t) become "1" (see the hatching in matrix g(t)) and the elements in rows other than the second row become "0", the estimation means 41A estimates the elements in the second column of matrix H(t) by receiving a pilot signal transmitted from one antenna of transmitter 1.

Similarly, when the element in the M _{T -th} row of matrix g(t) becomes "1" (see the hatching in matrix g(t)) and the elements in rows other than the M _T- th row become "0" at t = M T, the estimation means 41A estimates the element in the M _T-th column of matrix H(t) by receiving a pilot signal transmitted from one antenna of the transmitter 1.

Subsequently, at t = M _T + 1 to 2M _T , when the elements of the first row, the (M _T + 1)th row to the M _T row, and the second M _T row of matrix g(t) sequentially become "1" (see the hatching of matrix g(t)), and the elements other than the first row, the (M _T + 1)th row to the M _T row, and the second M _T row sequentially become "0", the estimation means 41A estimates the superposition elements H _1,MT+1 , H _2,MT+2 , ..., H _MT,2MT of the two columns of matrix H(t), respectively.

The superposition element _H1,MT+1 is an element obtained by superposing the elements of the first column and the ( _MT +1)th column of the matrix H(t), the superposition element _H2,MT+2 is an element obtained by superposing the elements of the second column and the ( _MT +2)th column of the matrix H(t), and so on, with the superposition element _HMT,2MT being an element obtained by superposing the elements of the _MTth column and the second MTth column of the matrix H( _t ).

The estimation means 41 then subtracts the already estimated element _H1 of the first column from the superimposed element H1 _,MT+1 to estimate the element HMT ₊₁ of the _M +1th column, subtracts the already estimated element _H2 of the second column from the superimposed element H2 _,MT+2 to estimate the element _{HMT +2} of the M+2th column, and similarly subtracts the already estimated element _HMT of the M- _th column from the superimposed element HMT _,2MT to estimate the element _H2MT of the second M- _th column.

Thereafter, in the same manner, for t = NM _T + 1 to (N+1) _MT , when the elements of the (NM _T + 1)th row to the (N+1) _MT row of matrix g(t) sequentially become "1" (see the hatching in matrix g(t)) and the elements other than the (NM _T + 1)th row to the (N+1) _MT row sequentially become "0", the estimation means 41A estimates the superposition elements H _1,NMT+1 , H _2,NMT+2 , ..., _{HMT, (N+1)MT} of the two columns of matrix H(t).

The superposition element _H1,NMT+1 is an element obtained by superposing the elements in the first column and the (NM _T + 1)th column of the matrix H(t), the superposition element _H2,NMT+2 is an element obtained by superposing the elements in the second column and the (NM _T + 2)th column of the matrix H(t), and similarly, the superposition element _HMT,(N+1)MT is an element obtained by superposing the elements in the M _Tth column and the (N+1) _MTth column of the matrix H(t).

Then, the estimation means 41 subtracts the already estimated element _H1 of the first column from the superimposed element H1 _,NMT+1 to estimate the element _HNMT+1 of the _NMT +1th column, subtracts the already estimated element _H2 of the second column from the superimposed element H2 _,NMT+2 to estimate the element _HNMT+2 of the _NMT +2th column, and similarly subtracts the already estimated element _HMT of the _MTT column from the superimposed element _HMT,(N+1)MT to estimate the element H _{(N+1)MT of the (N+1) MT} column.

Figure 16 is a conceptual diagram showing the components of matrix g(t). Referring to Figure 16, matrix g(t) is composed of a unit matrix I and a reflection coefficient matrix Θ arranged vertically as [I^T Θ^T]^T.

The identity matrix I is a matrix whose diagonal elements are "1". The reflection coefficient matrix Θ is a matrix whose diagonal elements are the reflection coefficient θ.

In FIG. 15, two elements of the matrix g(t) are "1" for t=M _T +1 to (N+1)M _T , and the reason for this is as follows.

15, the elements of matrix g(t) that are "1" move sequentially from the first column to the M _{- th} column. As a result, the elements of matrix g(t) that are "1" are switched sequentially along the diagonal elements of unit matrix I that are "1" shown in FIG.

In addition, for t = M _T + 1 to (N+1)M _T shown in FIG. 15, the elements of matrix g(t) that become "1" are the elements of [the elements in the first column and the (M _T + 1)th column] to [the elements in the M _T column and the (N+1)M _T column].

The unit matrix I shown in FIG. 16 has M _T rows and M _T columns, so for t = M _T +1 to (N+1)M _T shown in FIG. 15, the elements of the matrix g(t) that become "1" are switched sequentially along the diagonal elements of the reflection coefficient matrix Θ shown in FIG. 16.

As a result, at t=M _T +1, when element θ (reflection coefficient element) in the first row and first column of the reflection coefficient matrix Θ is set to "1," a "1" in the unit matrix I exists in the same first column. Since the "1" in the unit matrix I cannot be controlled by IRS2A, at t=M _T +1, the element in the first column and the element in the (M _T +1)th column of matrix g(t) become "1." For t=M _T +2 to (N+1)M _T , for the same reason, two elements of matrix g(t) become "1."

Therefore, the estimation means 41A subtracts the estimated values already estimated at t=1 to MT from the estimated values estimated at t= _MT +1 to (N+1) _MT , and estimates the subtraction results as the estimated values at _{t=MT +} 1 to (N+1) _MT .

Figure 17 is a diagram illustrating the problems that arise when estimating the channel frequency response matrix H(t) using the method shown in Figure 15.

Referring to Figure 17, when matrix H(t) is estimated using the method shown in Figure 15, during training period TRN_1, the acquisition time of the propagation path estimate value EST_1_1 in the first column of matrix H(t) is different from the acquisition time of the propagation path estimate value EST_(N+1) _{MT_1} in the (N+1) _MT column of matrix H(t), and during training period TRN_2, the acquisition time of the propagation path estimate value EST_1_2 in the first column of matrix (t) is different from the acquisition time of the propagation path estimate value EST_(N+1) _{MT_2} in the (N+1) _MT column of matrix (t) (see (a) of Figure 17).

Furthermore, when using a method such as index modulation, which does not always use all transmitting antennas, there are situations where an estimate cannot be obtained for a specific OFDM symbol or radio frame. Index modulation is a modulation method that assigns information to the selection pattern used when selecting a specific element from an arbitrary set and transmits it.

In the second embodiment, the transmitter 1 selects one antenna from the M _T antennas of the transmitter 1, and when transmitting one pilot signal using the selected antenna, changes the antenna pattern of the M _T antennas to (N+1) M _T antenna patterns by changing the antenna used to transmit the pilot signal, and sequentially transmits (N+1) M _T pilot signals.

As a result, each of the (N+1)M _T pilot signals is assigned to an antenna pattern in which only one antenna out of the M _T antennas is used to transmit the pilot signal.

Therefore, the transmitter 1 sequentially transmits (N+1) _MT pilot signals by index modulation.

In this case, even if estimates are obtained for t = 1 to (N + 1) _MT in the training period TRN_1, estimates may not be obtained for t = (N + 1) _MT in the training period TRN_2 (see (b) in Figure 17). That is, elements of the matrix H(t) estimated by the method shown in Figure 15 may be missing.

Therefore, matrix interpolation is applied to the matrix H(t) estimated using the method shown in Figure 15. Since the missing elements in matrix H(t) are random, a method is adopted to estimate the entire matrix H(t) from randomly missing time series data.

Note that index modulation involves allocating and transmitting pilot signals to antenna patterns of M _T antennas, in which only one antenna among M _T antennas is used to transmit the pilot signal, and antennas other than the one antenna are not used to transmit the pilot signal.

18 is a diagram illustrating a method for extracting elements of the estimated matrix H(t). Referring to FIG. 18, in the time-series data D_chr, estimated values of the matrix H(t) are indicated by black circles (●). Of the data indicated by black circles (●), the data estimated when t = M _T +1 to (N+1)M _T consists of the subtraction results obtained by subtracting the superimposed elements, as described above.

The estimation means 41A moves the sliding window in the direction of the arrow, and extracts a portion of data from the time-series data D_chr using the sliding window for each t shown in FIG. 15 for all of t = 1 to (N+1) _MT , and generates a Hankel matrix R by stacking the extracted (N+1) _MT row vectors.

Figure 19 is a conceptual diagram showing matrix decomposition. Referring to Figure 19, the estimation means 41A decomposes the generated Hankel matrix R into the product PQ of matrix P and matrix Q.

If a matrix has low rank, it can be expressed as the product of two low-rank matrices. Here, for example, a matrix is said to be low rank if its rank is 1/10 of the smaller of the number of rows and the number of columns.

An element R _i,j of a Hankel matrix R is expressed as the product of an element P _i,: of a matrix P and an element Q _:,k of a matrix Q, where the notation "P _i,: " represents the i row of the matrix P, and the notation "Q _:,k " represents the k column of the matrix Q.

Then, we set up the optimization problem shown in equation (27).

In equation (27A), J ₁ (P, Q) is expressed by equation (27B), J ₂ (P, Q) is expressed by equation (27C), and λ is a regularization parameter, for example, 10 ⁻³ .

And λJ ₂ (P,Q) is a regularization term to prevent overfitting. Also, on the right side of equation (27B), |R _i,j -P _i,: Q _:,k | is an error term for each element, and "Ψ" is a set of indices of known points. Furthermore, on the right side of equation (27C), "2" is a norm constraint, and "F" is the Frobenius norm, which indicates that all elements are squared and added together, and the square root of the sum is calculated.

The optimization shown in equation (27A) determines P and Q that minimize the error.

20 is a diagram showing the optimization algorithm. Referring to FIG. 20, first, R(0), Ψ, L, λ, and t _max are set.

Then, in "2:" to "4:", the initial values of matrices P and Q are given by singular value decomposition. Also, in "7:" to "12:", each row of matrix Q is updated. Furthermore, in "13:" to "18:", each row of matrix P is updated. Furthermore, in "20:" to "21:", matrix R is updated.

Furthermore, "11:" corresponds to performing interpolation in matrix Q, and "17:" corresponds to performing interpolation in matrix P.

The above "updating each row of matrix Q,""updating each row of matrix P," and "updating matrix R" are repeatedly executed when t< _tmax , and the optimization algorithm ends when t= _tmax , where _tmax is, for example, 200.

21 is a diagram showing a selection matrix. Referring to FIG. 21, the selection matrix S _k has one "1" in each row and the rest are "0". When the matrix R includes four known parts, the selection matrix S _k extracts only the four known parts in the kth column of the matrix R.

To extract a known part using selection matrix S _k , at "9:" in Fig. 20, a known part is extracted from matrix P, and the extracted part is designated P _part . Then, at "10:", a known part is extracted from column k of matrix R using selection matrix S _k , and the extracted known part is designated x. Then, at "11:", the rows of matrix Q are updated.

The same is done for "15:", "16:", and "17:" using the selection matrix S _i .

Therefore, matrix interpolation is performed using the optimization algorithm shown in Figure 20.

Figure 22 is a diagram illustrating how to reconstruct a time series from an interpolated Hankel matrix R.

22 , the average value of multiple estimated values included in the anti-diagonal element EL_1 of the missing Hankel matrix R ^* (t) estimated by matrix interpolation is calculated, and the calculated average value of the estimated values is restored as interpolated time series data, for all of the anti-diagonal elements EL_1 to EL_V of the Hankel matrix H ^* (t). In this way, the interpolated time series is restored.

Note that each of the anti-diagonal elements EL_1 to EL_V consists of elements from the same point in time, so the average value can be restored as an element at a single point in time in the time series.

The estimation means 41A receives received signals of (N+1) _MT pilot signals transmitted from the transmitter 1 using the above-mentioned method, and estimates the (N+1) _MT columns of the matrix H(t) to estimate the matrix H(t), generates a Hankel matrix R from the estimated matrix H(t), decomposes the generated Hankel matrix R into a product PQ of matrices P and Q, performs matrix interpolation based on the decomposed product PQ to obtain a Hankel matrix R ^* (t) with no missing elements, and estimates the time series reconstructed based on the obtained Hankel matrix R ^* (t) as the frequency response matrix H ^* (t).

Then, after estimating the matrix H ^* (t), the estimation means 41A sets the estimated frequency response matrix H ^* (t) as the frequency response FQR_0 of the propagation path at the time of reception _t0 , and uses the frequency response FQR_0 to estimate frequency responses FQR_1 to FQR_G at times _t1 to _tG that are later than the time of reception _t0 using the same method as the estimation means 41, and outputs the frequency responses FQR_0 to the optimization means 42.

Figure 23 is a flowchart for explaining the operation of the estimation device 4A shown in Figure 12. The flowchart shown in Figure 23 is the same as the flowchart shown in Figure 6, except that steps S1 to S3 of the flowchart shown in Figure 6 are replaced with steps S21 to S23.

Referring to FIG. 23 , when the operation of the estimation device 4A is started, when the transmitter 1 sequentially changes the antenna patterns of the M _T antennas in index modulation to (N+1) M _T antenna patterns and sequentially transmits (N+1) M _T pilot signals, the estimation means 41A of the estimation device 4A sequentially estimates (N+1) M _T columns of a frequency response matrix H( _t ) indicating the frequency response of the propagation path between the transmitter 1 and the receiver 3A by sequentially receiving (N+1) M T received signals of the (N+1) M _T pilot signals from the communication means 32 of the receiver 3A (step S21).

Then, the estimation means 41A generates a Hankel matrix R from the frequency response matrix H(t) by the above-mentioned method (step S22). Thereafter, the estimation means 41A decomposes the Hankel matrix R into a product PQ of matrices P and Q, performs matrix interpolation using the decomposed product PQ, estimates a time series restored based on the Hankel matrix R ^* after matrix interpolation as a frequency response matrix H ^* (t), and estimates the frequency response matrix H ^* (t) as a frequency response FQR_0 at the reception time _t0 (step S23).

Then, the estimation means 41A sequentially executes steps S4 to S10 described above, and the optimization means 42 sequentially executes steps S11 and S12 described above. This completes the operation of the estimation device 4A.

Figure 24 is a flowchart for explaining the detailed operation of step S21 in Figure 23. Referring to Figure 23, when operation of the estimation device 4A starts, the estimation means 41A of the estimation device 4A sets t = 1 (step S211).

The estimation means 41A then estimates the element h_t in the t-th column of the frequency response matrix H(t) by receiving one received signal r_t from the communication means 32 of the receiver 3A (step S212).

Thereafter, the estimation means 41A determines whether or not t≧M _T +1 holds (step S213).

If it is determined in step S213 that t is not equal to or greater than M _T +1, the estimation means 41A sets t to t +1 (step S214). Thereafter, the operation of the estimation device 4A proceeds to step S212, and steps S212 to S214 are repeatedly executed until it is determined in step S213 that t is equal to or greater than M _T +1.

Then, when it is determined in step S213 that t≧M _T +1, the estimation means 41A calculates q=mod(t, M _T ) (step S215), where q is the remainder when "t" is divided by "M _T ".

Then, the estimation means 41A determines whether q = 0 (step S216). If it is determined in step S216 that q = 0 is not true, the estimation means 41A obtains the estimated value h_q of the qth column from the already estimated values, subtracts the estimated value h_q of the qth column from the superposition element h_sip_t of the tth column, and estimates the subtraction result as the element h_t of the tth column (step S217).

On the other hand, when it is determined in step S216 that q = 0, the estimation means 41A obtains an estimated value _{h_MT} of the M _T-th column from the estimated values that have already been estimated, subtracts the estimated value _{h_MT} of the M _T-th column from the superposition element h_sip_t of the t-th column, and estimates the subtraction result as the element h_t of the t-th column (step S218).

After step S217 or step S218, the estimation means 41A determines whether t=(N+1) _MT (step S219).

When it is determined in step S219 that t is not (N+1) _MT , the estimation means 41A sets t to t+1 (step S220). Thereafter, the operation of the estimation device 4A proceeds to step S212, and steps S212 and S213 (YES), and steps S215 to S220 are repeatedly executed until it is determined in step S219 that t is (N+1) _MT .

Then, if it is determined in step S219 that t=(N+1) _MT , the operation of the estimation device 4A proceeds to step S22 in FIG.

In the flowchart shown in FIG. 24, when t=1 to M _T , steps S212, "NO" in S213, and S214 are repeatedly executed, and in step S212, elements h_1 to h_M _T in the first to M _T columns of the frequency response matrix H(t) are estimated (see t=1 to M _T in FIG. 15).

When t≧M _T +1, in step S212, the estimated element h_t of the t-th column is made up of a superimposed element in which two elements are superimposed.

Therefore, in step S213, when it is determined that t≧M _T +1, q=mod(t, M _T ) is calculated, and when q is not 0, that is, when q=1 to M _T −1, the element h_q in the q (=1)-th column is subtracted from the superposition element h_sip_t in the M _T +1-th column where t=M _T +1, and the subtraction result is estimated as the element h_t in the t-th column (see step S217). When t=M _T +2 to 2M _T −1 in FIG. 15, the element h_t in the t-th column is estimated in a similar manner.

Also, when t=NM _T +1 to (N+1)M _T −1 in FIG. 15, the element h_t of the t-th column is estimated in the same manner.

On the other hand, when q = 0, the q (= M _T ) element h_q (= M _T ) is subtracted from the superposition element h_sip_t of the second M _T column where t = 2M _T , and the subtraction result is estimated as the element h_t of the t column (see step S218). When t = (N + 1) M _T in Figure 15, the element h_t of the t column is estimated in a similar manner.

As a result, for t=M _T +1 to (N+1)M _T in FIG. 15, the subtraction results obtained by subtracting the superimposed estimated values can be estimated as elements of the M _T +1 to (N+1)M _T columns.

Figure 25 is a flowchart explaining the detailed operation of step S23 in Figure 23.

Referring to FIG. 25, after step S22 in FIG. 23, the estimation means 41A performs singular value decomposition (svd(R)) on the Hankel matrix R to decompose it into the product PQ of matrices P and Q, and provides initial values for matrices P and Q (step S231). More specifically, the estimation means 41A sequentially executes "2:" to "4:" in FIG. 20 to provide initial values for matrices P and Q.

Then, the estimation means 41A sets t ^up =0 (step S232), where t ^up is an index indicating the number of times the matrices P, Q, and R are updated, and is an integer that satisfies 1≦t ^up ≦t ^up _max , and t ^up _max is the maximum number of times the matrices P, Q, and R are updated.

After step S232, the estimation means 41A sequentially executes "7:" to "12:" in Figure 20 to update matrix Q (step S233), sequentially executes "13:" to "18:" in Figure 20 to update matrix P (step S234), and sequentially executes "20:" to "21:" in Figure 20 to update Hankel matrix R (step S235).

Subsequently, the estimation means 41A sets t ^up =t ^up +1 (step S236), and then determines whether t ^up <t ^up _max (step S237).

When it is determined in step S237 that t ^up < t ^up _max , the operation of the estimation device 4A proceeds to step S233, and steps S233 to S237 are repeatedly executed until it is determined in step S237 that t ^up < t ^up _max does not hold.

Then, if it is determined in step S237 that t ^up <t ^up _max does not hold, the estimation means 41A restores the Hankel matrix R ^* after matrix interpolation in time series by the method described above (step S238).

Thereafter, the estimation means 41A estimates the restored time series as a frequency response matrix H ^* (t) (step S239), and estimates the frequency response matrix H ^* (t) as a frequency response FQR_0 at the time of reception _t0 (step S240). Thereafter, the operation of the estimation device 4A proceeds to step S4 in FIG.

According to the flowchart shown in FIG. 23 (including the flowcharts shown in FIGS. 7 to 9 and the flowcharts shown in FIGS. 24 and 25 ), when the transmitter 1 sequentially changes the antenna patterns of the M _T antennas in index modulation to (N+1) M _T antenna patterns and sequentially transmits (N+1) M _T pilot signals, the estimation device 4A sequentially receives (N+1) M _T received signals of the (N+1) M _T pilot signals from the communication means 32 of the receiver 3A, thereby estimating (N+1) M T columns of a frequency response matrix H(t) indicating the frequency response of the propagation path between the transmitter 1 and the receiver 3A (see step S21), performs _matrix interpolation on the frequency response matrix H(t) to estimate a frequency response FQR_0 of the propagation path at the time of reception _t0 (see step S23), and estimates a frequency response FQR_0 of the propagation path at a time t that is later than the time of reception _t0 from the frequency response FQR_0 of the propagation path. ₁ , the frequency response FQR_1 of the propagation path is estimated (see step S6), the frequency response FQR_2 of the propagation path is estimated from the frequency response FQR_1 of the propagation path, the frequency response FQR_3 of the propagation path is estimated from the frequency response FQR_2 of the propagation path, the frequency response FQR_4 of the propagation path is estimated from the frequency response FQR_3 of the propagation path, ... and similarly, the frequency response FQR_G of the propagation path is estimated from the frequency response FQR_G-1 of the propagation path (see steps S8 to S10).

Then, similar to the estimation device 4, the estimation device 4A repeatedly estimates the frequency response FQR_g at time _tg to the frequency response FQR_g+ _{1 at time tg+1} using equations (18) and (22), thereby estimating the frequency responses FQR_2 to FQR_G at times _t2 to _tG , respectively (see steps S8 to S10).

Therefore, by setting the times t ₁ to t _G to the times of signal transmission, it is possible to suppress the discrepancy due to the lag between the estimated time of the propagation path between the transmitter 1 and the receiver 3A and the transmission time.

In addition, the estimation device 4A estimates the frequency response FQR_0 by performing matrix interpolation on the frequency response matrix H(t), so it can estimate the frequency response FQR_0 without missing elements. As a result, the estimation device 4A can use the frequency response FQR_0 to estimate the frequency responses FQR_1 to FQR_G without missing elements.

Other effects described in embodiment 1 can also be obtained.

In the second embodiment, the operation of the estimation device 4A may be realized by software. In this case, the estimation device 4A includes a CPU, ROM, and RAM. The ROM stores a program Prog_B consisting of the steps of the flowchart shown in FIG. 23 (including the flowcharts shown in FIGS. 7 to 9 and the flowcharts shown in FIGS. 24 and 25).

The CPU reads out the program Prog_B from the ROM and executes the read out program Prog_B to estimate frequency responses FQR_0 to FQR_G from time t ₀ to t _G , and optimizes the transmission weights W and the reflection coefficients θ from time t ₀ to t _G using the frequency responses FQR_0 to FQR_G, and feeds back the optimized transmission weights W and the reflection coefficients θ to the transmitter 1 and the IRS 2 A, respectively. The RAM temporarily stores a codebook including patterns of ^QN reflection coefficients for the N reflecting elements 21.

Furthermore, the program Prog_B may be recorded on a recording medium such as a CD, a DVD, etc. and distributed. When a recording medium on which the program Prog_B is recorded is attached to a computer, the computer reads and executes the program Prog_B from the recording medium to estimate frequency responses FQR_0 to FQR_G from time t ₀ to t _G , and optimizes the transmission weights W and the reflection coefficients θ from time t ₀ to t _G using the frequency responses FQR_0 to FQR_G, and feeds back the optimized transmission weights W and reflection coefficients θ to the transmitter 1 and the IRS 2A, respectively.

Therefore, the recording medium on which the program Prog_B is recorded is a computer-readable recording medium.

In embodiment 2, the N reflective elements 21 described in embodiment 1 may be classified into c clusters.

In this case, when estimating each column of the frequency response matrix H(t) using the method described in Figure 15, the IRS controller 22A of the IRS 2A controls the one representative reflecting element to be turned "ON" in a predetermined order so that only one representative reflecting element out of the c representative reflecting elements of the c clusters is turned "ON" and the other (c-1) representative reflecting elements are turned "OFF."

The rest of the explanation for embodiment 2 is the same as the explanation for embodiment 1.

In the above-described first embodiment, it has been explained that the estimation device 4 calculates the frequency responses H D and H ^C of the propagation path using equations (1) to (6) based on the received signal y(t) of the pilot signal received from the receiver ³ , estimates the frequency response FQR_0 of the propagation path at the time t ₀ when the received signal y(t) is received, and uses the estimated frequency response FQR_0 to estimate the frequency responses FQR_1 to FQR_G at times t ₁ to t _G that are later than the time t ₀ when the received signal is received.

In the above-described second embodiment, it has been explained that when the transmitter 1 sequentially changes the antenna patterns of the M _T antennas in index modulation to (N+1)M _T antenna patterns and sequentially transmits (N+1)M _T pilot signals, the estimation device 4A sequentially receives (N+1)M _T received signals of the (N+1)M _T pilot signals from the communication means 32 of the receiver 3A, thereby sequentially estimating (N+1)M _T columns of the frequency response matrix H(t) indicating the frequency response of the propagation path between the transmitter 1 and the receiver 3A, performs matrix interpolation on the frequency response matrix H(t) to estimate the frequency response FQR_0 of the propagation path at the time of reception _t0 , and uses the estimated frequency response FQR_0 of the propagation path to estimate frequency responses FQR_1 to FQR_G at time points _t1 to _tG that are later than the time of reception _t0 .

Then, sequentially estimating the (N+1)MT columns of the frequency response matrix H(t) by sequentially receiving (N+1) _MT received signals of the (N+1) _MT pilot signals from the communication means 32 of the receiver _3A corresponds to estimating the frequency response matrix H(t) based on the pilot signals.

Furthermore, even if matrix interpolation is not performed on the frequency response matrix H(t), it is possible to use the frequency response matrix H(t) before matrix interpolation as the frequency response FQR_0, and use the frequency response FQR_0 to sequentially estimate the frequency responses FQR_1 to FQR_G using equations (18) and (22).

Therefore, the estimation device according to the embodiment of the present invention
In a wireless communication space in which a transmitter having M _T (M _T is an integer of 2 or more) antennas, an IRS which is an electromagnetic wave reflector having N (N is an integer of 2 or more) reflecting elements whose reflection characteristics can be dynamically changed, and a receiver having M _R (M _R is an integer of 2 or more) antennas are non-linearly arranged, when the transmitter transmits a pilot signal which is a known signal to the receiver, an estimation device is provided which estimates a frequency response of a propagation path between the transmitter and the receiver at the receiver,
an estimation means for, upon receiving a received signal of a pilot signal, estimating a frequency response FQR_0 of a propagation path based on the received signal, and using an autoregressive model to execute an estimation process for estimating G frequency responses FQR_1 to FQR_G, which are frequency responses at G future points in time from the point in time when the receiver receives the received signal (G is an integer equal to or greater than 1 and is the total number of points in time at which the frequency responses of the propagation path are estimated);
It is only necessary to provide an optimization means for performing an optimization process that optimizes the reflection coefficients of the N reflecting elements and the transmission weights of the M _T antennas using the frequency response FQR_0 and G frequency responses FQR_1 to FQR_G.

If the estimation device is equipped with an estimation means and an optimization means, it estimates the frequency response FQR_0 of the propagation path at the time of reception _t0 and the frequency responses FQR_1 to FQR_G of the propagation path at times _t1 to _tG that are later than the time of reception _t0 , and uses the estimated frequency responses FQR_0 to FQR_G to optimize the reflection coefficients of the N reflecting elements and the transmission weights of the M _T antennas, so that at each time point _t1 to _tG , it is possible to transmit a signal while suppressing the deviation due to the lag between the estimated time of the propagation path and the transmission time.

Furthermore, the program according to the embodiment of the present invention is
A program for causing a _computer to execute, in an estimation device of a _receiver , an estimation of a frequency response of a propagation path between a transmitter and a receiver when the transmitter transmits a pilot signal, which is a known signal, in a wireless communication space in which a transmitter having M _T (M _T is an integer of 2 or more) antennas, an IRS which is an electromagnetic wave reflector having N (N is an integer of 2 or more) reflecting elements whose reflection characteristics can be dynamically changed, and a receiver having M R (M R is an integer of 2 or more) antennas are non-linearly arranged,
a first step of executing an estimation process in which, when an estimation means receives a received signal of a pilot signal, it estimates a frequency response FQR_0 of a propagation path based on the received signal, and, based on the estimated frequency response FQR_0, it uses an autoregressive model to estimate G frequency responses FQR_1 to FQR_G which are frequency responses at G (G is an integer equal to or greater than 1 and is the total number of times at which the frequency responses of the propagation path are estimated) time points in the future from the time point at which the receiver receives the received signal;
and a second step in which the optimization means performs an optimization process to optimize the reflection coefficients of the N reflecting elements and the transmission weights of the M _T antennas using the frequency response FQR_0 and G frequency responses FQR_1 to FQR_G.

When the program causes a computer to execute the first step and the second step, it estimates the frequency response FQR_0 of the propagation path at the time of reception _t0 and the frequency responses FQR_1 to FQR_G of the propagation path at times _t1 to _tG that are later than the time of reception _t0 , and optimizes the reflection coefficients of the N reflecting elements and the transmission weights of the M _T antennas using the estimated frequency responses FQR_0 to FQR_G, so that at each time point _t1 to _tG , it is possible to transmit a signal while suppressing the deviation due to the lag between the estimated time of the propagation path and the transmission time.

In this embodiment of the present invention, the optimization means 42 that feeds back the optimized transmission weights W _{opt — 0} to W _{opt — G} shown in Table 1 and the optimized reflection coefficients θ _{opt — 0} to θ _{opt — G} shown in Table 2 to the transmitter 1 and IRS2 (or IRS2A), respectively, constitutes a ``feedback means.''

Furthermore, in this embodiment of the present invention, matrix Q constitutes the "first matrix" and matrix P constitutes the "second matrix."

Furthermore, in this embodiment of the present invention, in step S3 of FIG. 6, the frequency response H ^D constitutes the "first frequency response" of the frequency response FQR_0, and the frequency response H ^C constitutes the "second frequency response" of the frequency response FQR_0.

Furthermore, in this embodiment of the present invention, the frequency response H ^D _g (g=1 to G−1) in step S82 of FIG. 8 constitutes the “first frequency response” of the frequency response FQR_g (g=1 to G−1), and the frequency response H ^C _g (g=1 to G−1) in step S81 of FIG. 8 constitutes the “second frequency response” of the frequency response FQR_g (g=1 to G−1).

Furthermore, in this embodiment of the present invention, the frequency response H ^D _g+1 (g=1 to G−1) in step S82 of FIG. 8 constitutes the “first frequency response” of the frequency response FQR_g+1 (g=1 to G−1), and the frequency response H ^C _g+1 (g=1 to G−1) in step S81 of FIG. 8 constitutes the “second frequency response” of the frequency response FQR_g+1 (g=1 to G−1).

The embodiments disclosed herein should be considered in all respects to be illustrative and not restrictive. The scope of the present invention is indicated by the claims, not by the description of the above embodiments, and is intended to include all modifications within the meaning and scope of the claims.

This invention applies to an estimation device, a wireless communication system including the same, and a program for causing a computer to execute the device.

1 Transmitter, 2, 2A IRS, 3, 3A Receiver, 4, 4A Estimation device, 10 Wireless communication system, 21 Reflection element, 22, 22A IRS controller, 31 Antenna, 32 Communication means, 41, 41A Estimation means, 42 Optimization means.

Claims (19)

In a wireless communication space in which a transmitter having M _T (M _T is an integer of 2 or more) antennas, an IRS which is an electromagnetic wave reflector having N (N is an integer of 2 or more) reflecting elements whose reflection characteristics can be dynamically changed, and a receiver having M _R (M _R is an integer of 2 or more) antennas are non-linearly arranged, when the transmitter transmits a pilot signal which is a known signal to the receiver, an estimation device is provided for estimating a frequency response of a propagation path between the transmitter and the receiver at the receiver, the device comprising:
an estimation means for executing an estimation process, when receiving a received signal of the pilot signal, estimating a frequency response FQR_0 of the propagation path at the time when the received signal was received based on the received signal, and estimating G frequency responses FQR_1 to FQR_G, which are the frequency responses at G time points (G is an integer equal to or greater than 1 and is the total number of time points at which the frequency responses of the propagation path are estimated) that are future time points from the time when the receiver received the received signal, using an autoregressive model based on the estimated frequency response FQR_0;
an optimization means for performing an optimization process to optimize the reflection coefficients of the N reflecting elements and the transmission weights of the M _T antennas using the frequency response FQR_0 and the G frequency responses FQR_1 to FQR_G. The estimation device of claim 1, wherein the estimation means, in the estimation process, sets the estimated frequency response FQR_0 as the initial value of the frequency response, estimates the first frequency response FQR_1 from the initial value, and then estimates the gth (g is an integer satisfying 1≦g≦(G-1)) frequency response FQR_g through the (g+1)th frequency response FRQ_g+1, sequentially executing this estimation process for all g = 1 to (G-1) to estimate the G frequency responses FQR_1 to FQR_G. the frequency response FQR_0 and each of the G frequency responses FQR_1 to FQR_G include a first frequency response indicating a frequency response of a direct link, which is a propagation path when a radio wave directly reaches the receiver from the transmitter, and a second frequency response indicating a frequency response of an indirect link, which is a propagation path when the radio wave reaches the receiver from the transmitter via the IRS, and each of the first frequency response and the second frequency response of the frequency response FQR_0 is set as an initial value;
3. The estimation device according to claim 2, wherein, in the estimation process, the estimation means estimates a first first frequency response from an initial value of the first frequency response of the estimated frequency response FQR_0 and estimates a first second frequency response from an initial value of the second frequency response of the estimated frequency response FQR_0, then estimates the (g+1)th first frequency response from the gth first frequency response, estimates the (g+1)th second frequency response from the gth second frequency response, estimates the gth frequency response FQR_g consisting of the gth first frequency response and the gth second frequency response, and estimates the (g+1)th frequency response FQR_g+1 consisting of the (g+1)th first frequency response and the (g+1)th second frequency response, sequentially for all of g = 1 to (G-1), thereby estimating the G frequency responses FQR_1 to FQR_G. 4. The estimation device according to claim 1, wherein when the transmitter sequentially transmits (N+1)M _{T pilot signals to the receiver by index modulation in which only one antenna out of the M T antennas} is used for transmitting the pilot signal and antennas other than the one _antenna are not used for transmitting the pilot signal, the estimation means estimates the frequency response matrix by performing a process of estimating one column of a frequency response matrix indicating a frequency response of the propagation path for each reception of the pilot signal, for all columns of the frequency response matrix, and estimates the frequency response FQR_0 consisting of the estimated frequency response matrix. 5. The estimation device according to claim 4, wherein the transmission of the (N+1)M _T pilot signals by the index modulation is performed by the transmitter sequentially changing antenna patterns of the M _T antennas in the index modulation to the (N+1)M _T antenna patterns and sequentially transmitting the (N+1)M _T pilot signals. The estimation device described in claim 4 or 5, wherein, in the estimation process, the estimation means performs matrix interpolation on the estimated frequency response matrix to interpolate between elements of the frequency response matrix, and estimates the frequency response matrix after the matrix interpolation as the frequency response FQR_0. The estimation device described in claim 6, wherein, in the estimation process, the estimation means generates a Hankel matrix from the estimated frequency response matrix, performs singular value decomposition on the generated Hankel matrix to decompose it into a product of a first and a second matrix, and performs updating of the first matrix, the second matrix, and the Hankel matrix a predetermined number of times to perform the matrix interpolation. The N reflecting elements are classified into c clusters (c is an integer equal to or greater than 1), each of which has the same frequency response of the propagation path;
The estimation device according to claim 1 , wherein the reflective elements included in each of the c clusters are controlled so that they have the same reflective characteristics. 9. The estimation device according to claim 1, further comprising: a feedback means for feeding back the reflection coefficients of the N reflecting elements and the transmission weights of the M _T antennas optimized by the optimization means to the IRS and the transmitter, respectively. A wireless communication system comprising the receiver, the transmitter, and the IRS, the receiver comprising the estimation device described in any one of claims 1 to 9. In a wireless communication space in which a transmitter having M _T antennas (M _T is an integer of 2 or more), an IRS which is an electromagnetic wave reflector having N (N is an integer of 2 or more) reflecting elements whose reflection characteristics can be dynamically changed, and a receiver having M _R antennas (M _R is an integer of 2 or more) are non-linearly arranged, when the transmitter transmits a pilot signal which is a known signal to the receiver, a program for causing a computer to execute an estimation device of the receiver to estimate a frequency response of a propagation path between the transmitter and the receiver, the program comprising:
a first step of executing an estimation process in which, when a received signal of the pilot signal is received , a frequency response FQR_0 of the propagation path at the time the received signal is received is estimated based on the received signal, and an autoregressive model is used based on the estimated frequency response FQR_0 to estimate G frequency responses FQR_1 to FQR_G , which are the frequency responses at G time points (G is an integer equal to or greater than 1 and is the total number of time points at which the frequency responses of the propagation path are estimated ) that are future time points from the time the received signal is received;
a second step of performing an optimization process in which the frequency response FQR_0 and the G frequency responses FQR_1 to FQR_G are used to optimize the reflection coefficients of the N reflecting elements and the transmission weights of the M _T antennas. 12. The program for causing a computer to execute the program according to claim 11, wherein, in the estimation process of the first step, the estimated frequency response FQR_0 is set as an initial value of the frequency response, and when the first frequency response FQR_1 is estimated from the initial value, an estimation process is performed in which a gth (g is an integer satisfying 1≦g≦(G−1))th frequency response FQR_g to a (g+1)th frequency response FRQ_g+1 are estimated , and the G frequency responses FQR_1 to FQR_G are estimated. the frequency response FQR_0 and each of the G frequency responses FQR_1 to FQR_G include a first frequency response indicating a frequency response of a direct link, which is a propagation path when a radio wave directly reaches the receiver from the transmitter, and a second frequency response indicating a frequency response of an indirect link, which is a propagation path when the radio wave reaches the receiver from the transmitter via the IRS, and each of the first frequency response and the second frequency response of the frequency response FQR_0 is set to an initial value;
In the estimation process of the first step, when a first first frequency response is estimated from an initial value of the first frequency response of the estimated frequency response FQR_0 and a first second frequency response is estimated from an initial value of the second frequency response of the estimated frequency response FQR_0 , the (g+1)-th first frequency response is estimated from the g-th first frequency response , and the (g+1)-th second frequency response is estimated from the g-th second frequency response, 13. The program for causing a computer to execute the program according to claim 12, wherein a process of estimating the gth frequency response FQR_g consisting of the gth first frequency response and the gth second frequency response and estimating the (g+1)th frequency response FQR_g +1 consisting of the (g+1)th first frequency response and the (g+1)th second frequency response is sequentially executed for all of g=1 to (G−1), thereby estimating the G frequency responses FQR_1 to FQR_G. 14. The program for causing a computer to execute the program according to claim 11 , wherein when the transmitter sequentially transmits (N+1)M _T pilot signals to the receiver by index modulation in which only one antenna among the M _T antennas is used for transmitting the pilot signal and antennas other than the one antenna are not used for transmitting the pilot signal, the transmitter assigns the pilot signals to antenna patterns of the M _T antennas and transmits the pilot signals, the estimation process of the first step estimates the frequency response matrix by performing a process of estimating one column of a frequency response matrix indicating a frequency response of the propagation path for each received pilot signal for all columns of the frequency response matrix, and the frequency response FQR_0 consisting of the estimated frequency response matrix is estimated . 15. The program to be executed by a computer according to claim 14, wherein the transmission of the (N+1)M _T pilot signals by the index modulation is performed by the transmitter sequentially changing antenna patterns of the M _T antennas in the index modulation to the (N+1)M _{T antenna} patterns and sequentially transmitting the (N+1)M T pilot signals. 16. The program for causing a computer to execute the program according to claim 14 or 15, wherein, in the estimation process of the first step, matrix interpolation is performed on the estimated frequency response matrix to interpolate between elements of the frequency response matrix, and the frequency response matrix after the matrix interpolation is estimated as the frequency response FQR_0. 17. The program for causing a computer to execute the program according to claim 16, wherein in the estimation process of the first step, a Hankel matrix is generated from the estimated frequency response matrix, the generated Hankel matrix is decomposed by singular value decomposition into a product of a first and a second matrix, and the matrix interpolation is performed by updating the first matrix , the second matrix, and the Hankel matrix a predetermined number of times. The N reflecting elements are classified into c clusters (c is an integer equal to or greater than 1), each of which has the same frequency response of the propagation path;
18. The program for causing a computer to execute the program according to claim 11, wherein the reflective elements included in each of the c clusters are controlled so that the reflective characteristics are the same. 19. The program for causing a computer to execute the program of claim 11, further causing the computer to execute a third step of feeding back the optimized reflection coefficients of the N reflecting elements and the optimized transmission weights of the M _T antennas to the IRS and the transmitter, respectively .